Question

if PA and PB all two tangents drawn to the circle with centre O such that angleBPA=120 degree,prove that OP=2PB.

Answer 1

now join OA and OB in figure

we know that here, < BPA + < AOB = 180

so here, < AOB = 60

now OP bisects < AOB, ∴ <AOP = <BOP = 30

now in Δ BOP,

sin 30 = PB/OP

1/2 = PB/OP

or simply OP = 2PB

Hence proved