Question

In the given figure, PCD is a secant to the circle with centre O from a point P outside the circle and PA is a tangent. If PA = 12 cm and PC = 7.2 cm, then the radius of the circle is

• A.
  16 cm
• B.
  4cm
• C.
  8cm
• D.
  6 cm

Answer 1

The correct option is C

8cm
Given that PA is the tangent to the circle and PCD is a secant to the circle.

$\therefore AO\perp PA$
(Angle between a tangent and the radius of a circle is 90°)



Apply Tangent Secant Theorem
$\therefore PC\times PD=P{A}^2\Rightarrow 7.2\times PD={12}^2\Rightarrow PD=20cm$

In $\Delta PAD,$ by Pythagoras theorem

$P{D}^2=P{A}^2+A{D}^2\Rightarrow {20}^2={12}^2+A{D}^2\Rightarrow A{D}^2=400-144=256\Rightarrow AD=16cm$

Thus, radius of the circle is 8 cm.

Hence, the correct answer is option c .