Question

Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle. Also ∠A + ∠C = 180°, then prove that the vertex D also lie on the same circle.

Answer 1

Given : ∠A + ∠C = 180° 

∴ ∠B + ∠D = 360° – 180° 

[ ∵ sum of the four angles of a quad. is 360 ]. 

Now in □ABCD, sum of the pairs of opp. angles is 180°. 

∴ □ABCD must be a cyclic quadrilateral, i.e., D also lie on the same circle on which the vertices A, B and C lie. Hence proved.