Question

In the figure, O is the centre of the circle of radius 13 cm and chord AB is of length 24 cm. If OC is perpendicular from the centre to AB, then the value of OC equals :

• A. 26 cm
• B. 10 cm
• C. 5 cm
• D. 8 cm

Answer 1

The correct option is C 5 cm

Perpendicular drawn from centre of a circle to chord bisects the chord.

$AC=BC=12cm$

And $\angle OCB={90}^{\circ }$

Thus, triangle OCB is a right angled triangle

$OB=13cm$.

Therefore by Pythagoras theorem

${OB}^2={OC}^2+{BC}^2$

${OC}^2={OB}^2-{BC}^2$

$OC$=$\sqrt{{13}^2-{12}^2}$

$OC=5cm$

option C will be the answer.