Question

In the figure , O is the centre of a circle of radius 9 cm. Semicircle with diameter OA cuts the circle at D.

If DP is perpendicular to OA and OA = 15 cm, then DP = _____ cm.

• A. 8.5 cm
• B. 6.2 cm
• C. 7.2 cm
• D. 7 cm

Answer 1

The correct option is C

7.2 cm

$\angle ODA={90}^{\circ }$ ............(angle in the semicircle)

$O{D}^2$ = OP $\times$ OA

$\Rightarrow$ 81 = OP $\times$ 15

OP = $\frac{81}{15}$

$△ODP\sim △DAP$ ........ (AA similarity)

$D{P}^2$ = OP $\times$ PA

= $\frac{81}{15}\times (15-\frac{81}{15})$

= $\frac{81}{15}\times \left(\frac{144}{15}\right)$

= $\frac{9^2\times {12}^2}{{15}^2}$

$\Rightarrow$ DP = $\frac{9\times 12}{15}$ = $\frac{36}{5}$ = 7.2 cm