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Question
If TP and TQ are two tangents to a circle with centre O from an external point T so that ∠ POQ = 120°, then ∠ PTQ is equal to ______.
Options
60°
70°
80°
90°
MCQ
Fill in the Blanks
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Solution
If TP and TQ are two tangents to a circle with centre O from an external point T so that ∠ POQ = 120°, then ∠ PTQ is equal to 60°.
Explanation:
The sum of angles in a quadrilateral is 360°.
∠ POQ + ∠ OPT + ∠ PTQ + ∠ OQT = 360°
120° + 90° + ∠ PTQ + 90 = 360°
300° + ∠ PTQ = 360°
∠ PTQ = 360° − 300°
∠ PTQ = 60°
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