Question

PA and PB are the tangents to a circle with centre O drawn from an external point p if angle APB=120° then show that OP=2AP
Hint : In ∆OAP, cos 60° = AP/OP

Answer 1

in tr.OAP and tr.OBP

op=op (common)

Oa=ob(radi of circle)

ap=pb(tangents of circle)

therr four tr.s ar congrant

oa=ap(CPCT)

OP=OA +AP(CPCT)

BUT WE KNOW. . OA=AP

OA=AP+AP

There four OA=2AP

Hence proved.....