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Question
In the given figure, PA is a tangent from an external point P to a circle with centre O. If ∠ POB = 125°, then ∠ APO is equal to:
Options
25°
65°
90°
35°
MCQ
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Solution
35°
Explanation:
The line segment AB is a diameter, so AOB is a straight line (diameter), the sum of angles on the line is 180°.
∠ AOP + ∠ POB = 180°
∠ AOP + 125° = 180°
= 180° − 125°
= 55°
According to the tangent property, the radius (OA) is perpendicular to the tangent (PA) at the point of contact.
∠ OAP = 90°
In Δ OAP, the sum of all angles is 180°.
∠ APO + ∠ OAP + ∠ AOP = 180°
∠ APO + 90° + 55° = 180°
∠ APO + 145° = 180°
∠ APO = 180° − 145°
∠ APO = 35°
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