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 ______.

 

पर्याय

• \[5\sqrt{2}\]
• \[10\sqrt{2}\]
• \[\frac{5}{\sqrt{2}}\]
• \[10\sqrt{3}\]

Answer 1

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

\[10\sqrt{2}\] cm.

Hence, the correct answer is option B.

Answer 2

Using pythagoras theorem in ΔABC, we get

BC² = AB² + AC²

= 10² + 10²

= 100 + 100

= 200

⇒ BC = `10sqrt(2)` cm