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Question
A chord of a circle of radius 10 cm subtends a right angle at the centre. The length of the chord (in cm) is
Options
- \[5\sqrt{2}\]
- \[10\sqrt{2}\]
- \[\frac{5}{\sqrt{2}}\]
- \[10\sqrt{3}\]
Solution
In right ∆OAB,
\[{AB}^2 = {OA}^2 + {OB}^2 \left( \text{Pythagoras Theorem} \right)\]
\[ \Rightarrow {AB}^2 = \left( 10 \right)^2 + \left( 10 \right)^2 \left( OA = OB = 10 cm \right)\]
\[ \Rightarrow {AB}^2 = 100 + 100 = 200\]
\[ \Rightarrow AB = \sqrt{200} = 10\sqrt{2} cm\]
Thus, the length of the chord is
Hence, the correct answer is option B.
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