Given that the vertices A, B, C of a quadrilateral ABCD lie on a circl

1.	Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle.Also ZA +ZC 180Â°, then prove that the vertex D also lie on the same circle.2.
Answer» Given. A+C=180° and A, B, C Lie on a circle To prove. D lies on the same circle as A, B, C. Soln. -- In a quadrilateral, if the sum of opposite angles is 180°, then it is a cyclic quadrilateral. In quad. ABCD, A + C=180°,Therefore, ABCD is a cyclic quad. In a cyclic quad., the vertices lie on the same circle. Thus, D also lies on the same circle..Hence, proved!

Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle.Also ZA +ZC 180Â°, then prove that the vertex D also lie on the same circle.2.

Answer»

Given. A+C=180° and A, B, C Lie on a circle

To prove. D lies on the same circle as A, B, C.

Soln. --

In a quadrilateral, if the sum of opposite angles is 180°, then it is a cyclic quadrilateral.

In quad. ABCD, A + C=180°,Therefore, ABCD is a cyclic quad.

In a cyclic quad., the vertices lie on the same circle. Thus, D also lies on the same circle..Hence, proved!