Question

Prove that the angles between the two tangents from an external pointto a circle is supplementary to the angle subtended by the line segments joining the points of contact to the center.

Answer 1

Given AB and AC are two tangents to a circle from an external point P. To prove∠A + ∠BOC = 180°  Proof By the theorem, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Hence ∠OBA = ÐOCA = 90° In a quadrilateral. ABOC, ∠A + ∠ACO + ∠COB + ∠OBA = 360° (Sum of the angles of a quadrilateral is 360°)

 ∠A + 90° + ∠COB + 90°  = 360° 

∠A + ∠BOC = 180

Answer 2

hey mate here is your answer in the pic
Hope it helps you
Thank you