Question

In the figure, O is the centre of a circle of radius 9 cm. Semicircle with Diameter OA cuts the circle at D and BC is a tangent through B.

If OA = 25 cm , then BC = ____.

• A. 15 cm
• B. 12 cm
• C. 16 cm
• D. 24 cm

Answer 1

The correct option is B

12 cm

$\angle OCA={90}^{\circ }$ ..........(angle in the semi circle)

$\angle OBC={90}^{\circ }$ ..........(Tangent is perpendicular to the radius at the point of contact)

\(\triangle OCB \sim \triangle CBA) ...........(AA similarity)

$\frac{OB}{CB}=\frac{CB}{AB}$ ...........(Sides opposite equal angles are proportional)

$C{B}^2$ = OB $\times$ AB

= 9 $\times$ 16

= $3^2\times 4^2$

$\therefore$ CB = 12 cm