Question

A chord of a circle of radius 10 cm subtends a right angle at its centre.The length of the chord (in cm) is.

• A. $5\sqrt{2}$
• B. $10\sqrt{2}$
• C. $\frac{5}{\sqrt{2}}$
• D. $10\sqrt{3}$

Answer 1

Answer: (B)

$10\sqrt{2}$

Consider a circle with centre at O, radius 10 cm. AB is the chord which subtends ${90}^{\circ }$ at the centre.
Now, In $△OAB$,
$O{A}^2+O{B}^2=A{B}^2$ (Using Pythagoras Theorem)
${10}^2+{10}^2=A{B}^2$
$A{B}^2=200$
$AB=10\sqrt{2}$