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A circle (with centre at O) is touching two intersecting lines AX and BY. The two points of contact A and B subtend an angle of 65° at any point C on the circumference of the circle. If P is the point of intersection of the two lines, then the measure of ∠APO is
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- 25°
- 65°
- 90°
- 40°
- 25°
Correct Option: A
As per the given in question , we draw a figure of a circle with centre O
Given , ∠ACB = 65°
We can say that angle subtended at the centre of a circled by an arc is twice to that at the circumference.
∠AOB = 2 × ∠ACB = 2 × 65° = 130°
∠OAP = 90°, ∠AOP = 65°
∴ ∠APO = 180° – 90° – 65° = 25°
