This is the defendant’s appeal from his conviction of one count of felony murder in violation of General Statutes § 53a-54c, one count of sexual assault in the first degree in violation of General Statutes § 53a-70 (a), and one count of burglary in the third degree in violation of General Statutes § 53a-103 (a).1 *449The issues on appeal are whether the trial court: (1) unduly restricted the cross-examination of the state’s primary witnesses; (2) improperly restricted the direct examination of the defendant’s primary witness thereby limiting the defendant’s right to present evidence; (3) improperly assumed the role of an advocate in issuing a cautionary instruction to the jury; (4) improperly failed to strike the testimony of Lisa Cozikowski; and (5) improperly instructed the jury as to the state’s burden of proof.
The jury might reasonably have found the following facts. On September 2, 1986, the victim was working alone on the 10:30 p.m. to 6:30 a.m. shift at her place of employment. Around 6:30 a.m. on September 3, a coworker found her dead, lying face down in an office, the victim of a massive blow to the head. In September, 1987, John Card and Marilu Flaler gave statements to the police that included unpublished details of the crime and implicated the defendant, Kenneth F. Ireland, Jr., Lee Magoon, and a third person known only as “Moe.” In their statements, Card and Flaler claimed that the defendant and Magoon had made incriminating remarks indicating their involvement in the crime during a conversation that occurred in the home shared by Card and Flaler on a Sunday afternoon shortly after the victim’s death.
The defendant was tried before a jury on November 27, 1989, which returned a verdict of guilty on all *450counts. On January 12,1990, the trial court sentenced the defendant to three terms of imprisonment: fifty years for felony murder; twenty years for first degree sexual assault; and five years for third degree burglary. The sentences were to run concurrently for a total effective sentence of fifty years.
I
The defendant first claims that the trial court improperly restricted his cross-examination of Card and Flaler, the state’s primary witnesses, in violation of his rights under the fifth, sixth and fourteenth amendments to the federal constitution, and article first, § 8 of the Connecticut constitution.2 The defendant claims that court-imposed limitations on his cross-examination of these crucial witnesses prevented him from proving the couple’s motive for incriminating the defendant, all in violation of his constitutionally protected right to confront the witnesses against him.
The defendant’s theory of the case was that Card and Flaler lied in an effort to protect Edmond Card, John Card’s brother, either because they believed that he was a suspect in the case or because he actually was involved in the murder. The defendant further theorized that the source of John Card and Flaler’s detailed information concerning the crime was not Magoon, but Edmond Card. In his cross-examination of John Card, the defendant’s attorney sought to establish that, at the time he gave incriminating evidence to the police, Card was aware that his brother was a suspect in the case. The state objected and out of the presence of the jury, Card denied knowing that his brother was a suspect. The trial court then sustained the state’s objection to this question being asked in the presence of the *451jury. It is this ruling that the defendant claims constituted the first impermissible limitation upon his right to confront the witnesses against him. We disagree.
“A defendant may give evidence concerning a third party’s involvement with the crime, as long as there is some evidence which directly connects the third party with the crime.” Siemon v. Stoughton, 184 Conn. 547, 555, 440 A.2d 210 (1981). “[I]t is within the sound discretion of the trial court to refuse to admit such evidence when it simply affords a possible ground of possible suspicion against another person.” State v. Giguere, 184 Conn. 400, 405, 439 A.2d 1040 (1981). Implicit in the attack on John Card’s alleged motive for implicating the defendant is the inference that Edmond Card was in fact involved in the crime. The defendant’s claim that Edmond Card was a suspect, or that John Card thought so, was never removed from the realm of counsel’s speculation, however, by the introduction of competent evidence or an offer of proof. To the contrary, a police detective testified, without contradiction, that Edmond Card was not a suspect at the time John Card provided his statement to the police. Furthermore, John Card testified that he was unaware that his brother was a suspect at that time. There was no other evidence brought to the trial court’s attention that remotely suggested that Edmond Card was involved in the murder or that John Card thought that was the case. Because there was no offer of proof to connect Edmond Card with the murder, or that John Card thought so, the trial court’s ruling was correct.
During cross-examination, Flaler acknowledged that she had given the police a statement in which she claimed that Magoon had talked to Edmond Card about the crime. The defendant’s counsel attempted to question Flaler as to the substance of the alleged conversation between Edmond Card and Magoon. The state objected to the line of questioning as being beyond the *452scope of direct examination. The trial court sustained the state’s objections. It is this ruling that forms the basis for the second part of the defendant’s claim that his right to cross-examine the state’s witnesses was impermissibly limited.
“It is well settled that our rule restricts cross-examination to matters covered in the direct examination, except as they involve credibility alone. State v. Zdanis, 173 Conn. 189, 195, 377 A.2d 275 (1977) .... Restrictions on the scope of cross-examination are within the sound discretion of the trial court.” State v. Sharpe, 195 Conn. 651, 657, 491 A.2d 345 (1985). A review of the transcript reveals that the subject matter of the questions on cross-examination did indeed exceed the scope of the direct examination of Flaler. Furthermore, what Magoon may have told Edmond Card was, at best, remote to this witness and, as the trial court pointed out, was more properly the subject of questions to be directed to Edmond Card who, in fact, did testify.
“The trial court has broad discretion to determine both the relevancy and remoteness of evidence. . . . Only upon a showing of a clear abuse of discretion will this court set aside on appeal rulings on evidentiary matters.” Dunham v. Dunham, 204 Conn. 303, 324, 528 A.2d 1123 (1987). Further, any statement by Flaler as to what Magoon told Edmond Card would have involved two levels of hearsay, i.e., what Magoon told Card and then what Card thereafter told Flaler. While the statements made by Magoon would likely have qualified as statements against penal interest and, therefore, arguably would have been within an exception to the rule against hearsay, defendant’s counsel offered no hearsay exception or nonhearsay use for the statement from Edmond Card to Flaler.
*453II
The defendant next claims that the trial court’s decision to limit his direct examination of Edmond Card restricted his right “ ‘to present a defense ... to the jury so that it may decide where the truth lies.’ ” State v. Kelly, 208 Conn. 365, 375, 545 A.2d 1048 (1988), quoting Washington v. Texas, 388 U.S. 14, 19, 87 S. Ct. 1920, 18 L. Ed. 2d 1019 (1967).
The defendant called Edmond Card as a defense witness. The state then filed a motion in limine seeking to preclude Edmond Card’s impeachment through use of two inconsistent statements that he had earlier given to the Wallingford police. In the first statement, given on September 4, 1987, Edmond Card claimed that Magoon had told him that he (Magoon), the defendant and a third person raped and murdered the victim. After a polygraph test indicated that the first statement was untrue, Edmond Card gave a second statement on September 9,1987, in which he disavowed the earlier statement and stated that Magoon had not said anything about the crime. He also stated that he had been with Magoon and the defendant on the night of the murder. Defense counsel claimed that proof of the two inconsistent statements bore on the issue of John Card’s and Flaler’s motives for testifying against the defendant, i.e., that they thought that Edmond Card was a suspect in the murder. The trial court granted the motion in limine in part and precluded the introduction of the two written statements as they were irrelevant to the issue of whether John Card and Flaler had motives for testifying. The trial court did, however, allow the defendant to question Edmond Card as to his whereabouts on the night of the murder and his relationship with Magoon and others. Edmond Card also testified that he gave two statements to the police and that there were inconsistencies between his first and second statements.
*454The defendant now argues that Edmond Card’s inconsistent statements should have been introduced as evidence of his consciousness of guilt as well as a basis for John Card’s and Flaler’s motivation for testifying. Consciousness of guilt was never advanced to the trial court as a reason for admitting the contradictory statements. It is fundamental that “counsel had the duty to state to the court the proper grounds for the admission of this evidence; Practice Book §§ 288, [4065 (d) (3)]; Acampora v. Ledewitz, 159 Conn. 377, 381, 269 A.2d 288 (1970). . . .” State v. Burns, 194 Conn. 469, 476, 481 A.2d 1077 (1984). Having failed to do so, a challenge to the trial court’s ruling based upon its failure to consider that reason, cannot be sustained. Acampora v. Ledewitz, supra.
“A trial judge may properly exclude questions, the relevancy of which appears to be slight and inconsequential and which would distract the jury from the main issues in the case.” State v. Moye, 214 Conn. 89, 96, 570 A.2d 209 (1990). The trial court found, and an examination of the transcript reveals, that none of Edmond Card’s statements in any way indicated that he was involved in the crime. In fact, his first statement to the police implicated the defendant, not himself. Since neither of the statements implicated Edmond Card, there was no possible linkage between Flaler’s and John Card’s motives for testifying. The trial court, therefore, correctly ruled that the statements were irrelevant.
Ill
The defendant next claims that the trial court’s comments to the jury had the effect of denying him his due process right to a fair trial. Following the November 15, 1989 proceedings, a juror overheard John Card tell Flaler that she had been “brilliant on the stand.” The juror communicated this remark to others on the jury. *455The defendant moved for a mistrial. The trial court denied the motion. Pointing out that John Card had not been present during Flaler’s testimony, the trial court instructed the jury “to ignore what was said and just remove it completely from your mind. ... I specifically instruct you to disregard the comment completely.” The defendant now claims that these remarks impermissibly supported John Card’s and Flaler’s integrity, bolstered their credibility and cast the trial court in the role of an advocate for the state’s position. Other than the bald assertion that this was the case, the defendant offers no reason, and we are unable to discern one, as to why a cautionary instruction to disregard a remark made by a witness somehow bolstered the credibility of that witness in the eyes of the jury and placed the trial court in the impermissible role of an advocate. This claim is without merit.
IV
The defendant next claims that the trial court improperly allowed the testimony of Lisa Cozikowski to stand. The defendant argues that Cozikowski’s testimony was unreliable, irrelevant and highly prejudicial and should have been excluded because it did not tend “to establish the existence of a material fact or to corroborate other direct evidence in the case.” State v. Sharpe, 195 Conn. 651, 659, 491 A.2d 345 (1985). Cozikowski testified that, approximately eighteen months after the murder, the defendant stated “Yeah, I did rape her” and “I killed her too.” Cozikowski testified that she was drunk at the time and may have imagined the statements. She testified further that she was unsure if the defendant was awake when he made the statements. The defendant moved to stike the testimony as being irrelevant. The trial court denied the motion.
“The trial court has broad discretion in determining the relevancy of evidence.” State v. Alvarez, 216 Conn. *456301, 309, 579 A.2d 515 (1990). “Evidence is admissible if it has ‘ “a reasonable tendency to prove or disprove a material fact in issue or shed some light upon some material inquiry. Note, 73 A.L.R.2d 769, 787.” State v. DeJesus, [194 Conn. 376, 381, 481 A.2d 1068 (1984)].’ State v. Doehrer, 200 Conn. 642, 649, 513 A.2d 58 (1986). There is no requirement that potentially inflammatory evidence be absolutely essential to the state’s case and otherwise unobtainable in order that it be admissible; rather, ‘ “the test for determining the admissibility of challenged evidence is relevancy and not necessity. State v. Piskorski, 177 Conn. 677, 701, 419 A.2d 866, cert. denied, 444 U.S. 935, 100 S. Ct. 283, 62 L. Ed. 2d 194 (1979).” State v. Haskins, 188 Conn. 432, 453, 450 A.2d 828 (1982) [cert. denied, 479 U.S. 1084, 107 S. Ct. 1285, 94 L. Ed. 2d 143 (1987)].’ State v. Doehrer, supra, 649.” State v. King, 216 Conn. 585, 603, 583 A.2d 896 (1990). We have never held that evidence is irrelevant simply because, standing on its own, it is insufficient to prove or disprove guilt. “Evidence is not rendered inadmissible simply because it is not conclusive. It is admissible if it tends to support a relevant fact even in a slight degree . . . .” State v. Morrill, 197 Conn. 507, 548, 498 A.2d 76 (1985).3
The defendant was on trial for a murder and sexual assault. The statements Cozikowski allegedly overheard described the defendant’s involvement in such acts. The trial court therefore reasonably could have concluded that the statements “Yeah, I did rape her” and “I killed her too” allegedly made by the defendant had a “tendency to prove ... a material fact in issue or shed some light upon” the defendant’s guilt or innocence. The trial court was therefore well within its discretion in determining that the evidence was relevant and that *457its probative value outweighed any prejudicial effect. The defendant’s concerns as to the intoxication of the witness and the general circumstances in which the statements were made go to the weight of the evidence and not its admissibility. State v. Morrill, supra, 548-49. In this regard, the trial court properly gave a thorough instruction to the jury regarding the weight of evidence and the credibility of witnesses which instruction was not challenged by the defendant.
Y
The defendant’s final claim is that the trial court’s instructions on reasonable doubt unconstitutionally diluted the state’s burden of proof. The trial court instructed the jury: “If, however, there is something in the evidence or lack of evidence which leaves in the minds of the jurors as reasonable men and women a reasonable doubt of the guilt of the accused as to any of these charges, a doubt for which if necessary you can give an explanation of to your fellow jurors in the jury deliberation room, then the defendant must be given the benefit of the doubt and found not guilty.”
We recently addressed a jury instruction claim similar to this one in State v. Johnson, 214 Conn. 161, 571 A.2d 79 (1990), and State v. Smith, 210 Conn. 132, 554 A.2d 713 (1989). In Johnson and Smith, “we disapproved of the instruction here at issue, but concluded that, according to federal precedent, it does not ‘constitute reversible error, let alone constitutional error in an otherwise adequate charge upon reasonable doubt.’ ” State v. Johnson, supra, 179, quoting State v. Smith, supra, 150. Since the instruction is not constitutionally defective, and since any other alleged error was not preserved at trial, we conclude that this claim must fail.
The judgment is affirmed.
In this opinion the other justices concurred.
General Statutes § 53a-54c provides: “felony murder. A person is guilty of murder when, acting either alone or with one or more persons, he commits or attempts to commit robbery, burglary, kidnapping, sexual assault in the first degree, sexual assault in the first degree with a firearm, sexual assault in the third degree, sexual assault in the third degree with a firearm, escape in the first degree, or escape in the second degree and, in the course of and in furtherance of such crime or of flight therefrom, he, or another participant, if any, causes the death of a person other than one of the participants, except that in any prosecution under this section, in which the defendant was not the only participant in the underlying crime, it shall be an affirmative defense that the defendant: (A) Did not conimit the homicidal act or in any way solicit, request, command, importune, cause or aid the commission thereof; and (B) was not armed with a deadly weapon, or any dangerous instrument; and (C) had no reasonable ground to believe that any other participant was armed with such a weapon or instrument; and (D) had no reasonable ground to believe that any other participant intended to engage in conduct likely to result in death or serious physical injury.”
General Statutes § 53a-70 (a) provides: “sexual assault in the first degree: class b felony: one year not suspendable. (a) A person is *449guilty of sexual assault in the first degree when such person (1) compels another person to engage in sexual intercourse by the use of force against such other person or a third person, or by the threat of use of force against such other person or against a third person which reasonably causes such person to fear physical injury to such person or a third person, or (2) engages in sexual intercourse with a person under thirteen years of age.”
General Statutes § 53a-103 (a) provides: “burglary in the third degree: class d felony, (a) A person is guilty of burglary in the third degree when he enters or remains unlawfully in a building with intent to commit a crime therein.”
We consider only the federal constitutional claims because the defendant offers no separate analysis under the state constitution.
“ ‘Relevant evidence’ means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.” Fed. R. Evid. 401.