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Question
In the given figure, PQ and PR are tangents to a circle with centre A. If ∠QPA = 27° then ∠QAR equals ______.
Options
63°
117°
126°
153°
MCQ
Fill in the Blanks
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Solution
In the given figure, PQ and PR are tangents to a circle with centre A. If ∠QPA = 27° then ∠QAR equals 126°.
Explanation:
∠QPR = 2∠QPA ...[∵ AP bisects ∠QPR]
= 2 × 27°
= 54°
Now, QPRA is a cyclic quadrilateral
⇒ ∠QAR + ∠QPR = 180°
⇒ ∠QAR = 180° – 54°
⇒ ∠QAR = 126°
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