Question

Two tagents PA and PB are drawn to a circle with centre o from an external point. Prove that angle APB=2times of angle OAB.

Answer 1

we know that

angle APB + angleAOB = 180 ( as solving quadrilateral all angles sum is 360)

OA = OB ( radius of circle )

angleOAB = angleOBA

angleOAB + angleOBC + angleAOB = 180 ( all sum of angle of triangle is 180)

angleOAB + angleOAB+ angle AOB = 180

angleAOB = 180 - 2angleOAB

as
angleAPB + angleBOA = 180

angleAPB + 180 - 2angleOAB= 180

angleAPB = 2angleOAB

I hope this solution will help you