Question

In the given figure, PQ and PR are tangents to a circle with centre A. If ∠QPA = 27° then ∠QAR equals ______.

विकल्प

• 63°

• 117°

• 126°

• 153°

Answer 1

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°