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$A B$ and $C D$ are two chords, that are 4 units, and 6 units respecti
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06 May 2025, 08:00
06 May 2025, 08:00
Expert Reply
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Question Stats:
66% (01:23) correct
33% (00:51) wrong based on 3 sessions
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$A B$ and $C D$ are two chords, that are 4 units, and 6 units respectively from the center..
GRE geometry circle.png [ 11.45 KiB | Viewed 183 times ]
Attachment:
GRE geometry circle.png [ 11.45 KiB | Viewed 183 times ]
Quantity A |
Quantity B |
CD |
AB |
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Re: $A B$ and $C D$ are two chords, that are 4 units, and 6 units respecti
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31 May 2025, 00:55
31 May 2025, 00:55
Expert Reply
\(\begin{aligned}
&\begin{aligned}
& \text { Column } \mathrm{A}=C D=2 \sqrt{r^2-6^2}=2 \sqrt{r^2-36} \\
& \text { Column } \mathrm{B}=A B=2 \sqrt{r^2-4^2} \\
& =2 \sqrt{r^2-16}
\end{aligned}\\
&\text { Therefore, } A B>C D \Rightarrow \text { Column } \mathrm{B}>\text { Column } \mathrm{A} \text {. Hence, the correct answer is } B \text {. }
\end{aligned}\)
&\begin{aligned}
& \text { Column } \mathrm{A}=C D=2 \sqrt{r^2-6^2}=2 \sqrt{r^2-36} \\
& \text { Column } \mathrm{B}=A B=2 \sqrt{r^2-4^2} \\
& =2 \sqrt{r^2-16}
\end{aligned}\\
&\text { Therefore, } A B>C D \Rightarrow \text { Column } \mathrm{B}>\text { Column } \mathrm{A} \text {. Hence, the correct answer is } B \text {. }
\end{aligned}\)
gmatclubot
Re: $A B$ and $C D$ are two chords, that are 4 units, and 6 units respecti [#permalink]
31 May 2025, 00:55
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