Question

In the figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR

Answer 1

Reflex angle POR= 2∠PQR 

= 2 × 100° = 200° 

Now, angle POR = 360° – 200 = 160° 

Also,

PO = OR [Radii of a circle] 

∠OPR = ∠ORP [Opposite angles of isosceles triangle] 

In ∆OPR, ∠POR = 160° 

∴ ∠OPR = ∠ORP = 10°