Question

Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Answer 1

Given, a quadrilateral ABCD circumference a circle with center O.

To prove: ∠AOB + ∠COD = 180°

And ∠AOD + ∠BOC = 180°

Join: OP, OQ,OR and OS.

We know that the tangents drawn from an external point of a circle subtend equal angles at the center.