The vertices of an △ ABC lie on a circle with centre O. AO is produced to meet the circle at the point P. D is a point on BC such that AD ⊥ BC. If ∠B = 68°, ∠C = 52°, then the measures of ∠ DAP is :
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 16°
∠BOA = 2 × 52 = 104°.
Now in △ABD,
68 + 90 + ∠BAD = 180
∠BAD = 180 - 90 - 68 = 22°
Here OA = OB so ∠OAB = ∠OBA
∠OAB = (180 - 104)/2 = 38°.
∠DAP = 38 - 22 = 16°.