In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons.

Topic: Circle theorems

Previous-year question practice database

Answer

Solution diagram

Exam answer

QR = OP (given) and OP = OQ (radii). Hence QR = OQ.

In ΔOQR: ∠ORQ = 20° ⇒ ∠QOR = 20°.

Therefore: ∠OQR = 180°−40° = 140°.

P,Q,R are collinear: ∠OQP = 180°−140° = 40°.

OP=OQ, so ΔOPQ is isosceles: ∠OPQ = 40°.

x = ∠POQ = 180°−80° = 100°.

Answer: x=100°.

Explanation

Use two isosceles triangles and the straight-line angle at Q.