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Question

In the given figure, PA and PB are two tangents to the circle with centre O. If APB=50°, then what is the measure of OAB ?


A
25°
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B
30°
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C
35°
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D
40°
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Solution

The correct option is A 25°
We know that tangents from an external point to a circle are equal.

So,
PA=PBPAB=PBA...(Angles opposite to equal sides are equal.)Now in triangle PAB, PAB+PBA+50°=180°2PAB+50°=180°PAB=65°

Since AP is a tangent to the circle,
OAP=90°OAB+PAB=90°OAB+65°=90°OAB=25°


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