Question

plz answer this question ​

Answer 1

Answer:

In figure OAPB

∠OAP = ∠OBP = 90° ( Line joining center and point of contact of tangent is perpendicular to tangent)

⇒ ∠OAP + ∠OBP = 90 + 90 = 180°

In figure OAPB

∠OAP + ∠APB + ∠PBO + ∠BOA = 360° ( Angle sum property of a quadrilateral)

90 + ∠APB + 90 + ∠BOA = 360°

∠APB + ∠BOA + 180 = 360

∠APB + ∠BOA = 360 - 180

⇒∠APB + ∠BOA = 180°

Since, opposite angles of the quadrilateral OAPB sum up to 180°

OAPB is a cyclic quadrilateral