Question

In the figure, O is the centre of the circle and PA is a tangent to it. The point P is 10 centimetres away from the centre of the circle. The diameter of the circle is 10 centimetres. <POA=

• A. 90⁰
• B. 30⁰
• C. 45⁰
• D. 60⁰

Answer 1

Answer:

D. 60⁰

From the figure:

• (OP = 10) cm

• Diameter (=10) cm, so radius (OA=5) cm.

• (PA) is tangent, so (OA\perp PA).

In right triangle (POA):

$\cos\angle POA=\frac{OA}{OP}=\frac{5}{10}=\frac12$

Therefore,

$\angle POA=60^\circ$

Answer: $(\boxed{60^\circ})$