If the angle between two tangents drawn from an external point P to a circle of radius a and center O, is 60o, then find the length of OP.

AP=BP (length of tangents from external point to circle are equal)
∠A=∠B=90o (Tangent is ⊥ to radius)
OP=OP (common side)
∴△AOP≅△BOP (RHS test of congruence)
∠APO=∠BPO=30o →c.a.c.t
∠AOP=∠BOP=60o →c.a.c.t
△AOP is 30o-60o-90o triangle.
∴△AOP, cos60=OA/OP
OP=a/12=2a