AB is the diameter of a circle with the center O. P as a point on it. If ∠AOP = 95° then find ∠OBP ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 47.5°.
Given that
AB is the diameter of a circle with the center O
∠AOP = 95°
∠BOP = 180° - 95° = 85°
OP = OB = radius = r
So, triangle OBP is a isosceles triagnle
∠B = ∠P = x
So,
∠BOP + ∠OBP + ∠OPB = 180°
⇒ 85° + x + x = 180°
⇒ x = 95°/2
⇒ x = 47.5°
⇒ ∠OBP = 47.5°