Question

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

Answer 1

If ∠PQR = 100°, then 

∠OPR = ? 

∠PQR = 100°. 

∴ ∠POR = ? 

∠POR = 2 × ∠PQR = 2 × 100° 

∠POR = 200° 

∴ ∠POR – Reflex angle 

∠POR = 360° 

∴ ∠POR = 360 – 200 

∴ ∠POR = 160° 

In ∆POR, 

OP = OR radii. 

∴ ∠OPR = ∠ORB 

∴ ∠OPR + ∠ORP + ∠POR = 180° 

∠OPR + ∠OPR + 160 = 180 

2∠OPR+ 160 = 180 

2∠OPR = 180 – 160 

2∠OPR = 20 

∠OPR = \(\frac{20}{2}\)

∴ ∠OPR= 10°.