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Radius $O A$ of a circle is perpendicular to the tangent $C A B$. If t
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02 May 2025, 03:40
02 May 2025, 03:40
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Radius $\(O A\)$ of a circle is perpendicular to the tangent $\(C A B\)$. If the length of $\(O A\)$ is 2 , then what is the ratio of $\(O C\)$ to $\(O B\)$ ?
(A) $\(\sqrt{2}: 4\)$
(B) $\(1: 3\)$
(C) $\(1: 2\)$
(D) $\(1: \sqrt{2}\)$
(E) $\(1: \sqrt{3}\)$
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Re: Radius $O A$ of a circle is perpendicular to the tangent $C A B$. If t
[#permalink]
07 May 2025, 05:00
07 May 2025, 05:00
Expert Reply
In the triangle $\(O A C, O C=2 \sqrt{2}\)$. Since the angles are in the ratio \(1:1:2\).
In the triangle $O A B, O C=4$ since the angles are in the ratio of \(1:2:3\).
Therfore, $\(O C: O B=2 \sqrt{2}: 4=1: \sqrt{2}\)$.
Thus, the correct answer is $D$.
In the triangle $O A B, O C=4$ since the angles are in the ratio of \(1:2:3\).
Therfore, $\(O C: O B=2 \sqrt{2}: 4=1: \sqrt{2}\)$.
Thus, the correct answer is $D$.
gmatclubot
Re: Radius $O A$ of a circle is perpendicular to the tangent $C A B$. If t [#permalink]
07 May 2025, 05:00
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