Question

if from an external point P of a circle with center o two tangent PA and PB are drawn such that angle B P A = 120 then show that of OP=2PA

Answer 1

angle BPA=120,
now, APB+AOB=180
120+AOB=180
AOB=180-120=60
In triangle OPA
Angle OPA=60as APB=120
OA is perpendicular on PA
Angle A =90
PA/OP=cos60
PA/OP=1/2
OP=2PA