Question

Two tangents PA and PB are drawn from the external point P of a circle with centre at O. If angle APO=30 degree, angle AOB= ?

Answer 1

In triangle APO an BPO we have
PA=PB ( tangents r equal)
OA=OB (radii of same circle)
PO=PO (common side)

∴ By SSS criteria triangle APO is congruent to triangle BPO
⇒∠APO = ∠BPO and ∠AOP = ∠BOP  ( by C.P.C.T)

∴∠APB = 2∠APO = 60°

But, ∠AOB + ∠APB = 180°
∴∠AOB = 180-60 = 120°

Answer 2

Angle AOB is equal to 120