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  1. 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
    1. 25°
    2. 65°
    3. 90°
    4. 40°
Correct Option: A

As per the given in question , we draw a figure circle with centre O ,

Given , ∠ACB = 65°
∠AOB = 2 × ∠ACB = 2 × 65° = 130°
∠OAP = 90°; ∠AOP = 65°
∴ ∠APO = 180° – 90° – 65° = 25°



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