Let A , B , C be three points on a circle of radius 1 such that ∠ A C B = π 4 . Then the length of the side A B is

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Question: Answered & Verified by Expert

Let

A, B, C

be three points on a circle of radius

1

such that

∠ A C B = \frac{π}{4}

. Then the length of the side

A B

is

MathematicsProperties of TrianglesKVPYKVPY 2020 (SA)

Options:

A $\sqrt{3}$
B $\frac{4}{3}$
C $\frac{3}{\sqrt{2}}$
D $\sqrt{2}$

Solution:

1105 Upvotes Verified Answer

The correct answer is:

\sqrt{2}

Let $O$ be the centre of the circle

In $Δ O A B$

$A B = \sqrt{2} r$ and $r = 1$

$\Rightarrow A B = \sqrt{2}$

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