If a diagnol of a cyclic quardilateral and diametre of a circle passing through the verticles of the quardilateral are same. Then prove that the quardilateral is a rectangle

Dear Student,



In cyclic quadrilateral all the four vertices will lie on the circumference of the circle.

Now, in a circle, taking any point on the circumference and connecting with the diameter will create a right angle triangle.

$$\begin{gathered} Thus, in △ABC, \\ \angle ABC is 90° \\ Similarly, in △ADC, \\ \angle ADC is 90° \\ Now, in △BAD, \\ \angle BAD is 90° \\ Similarly, in △BCD, \\ \angle BCD is 90° \end{gathered}$$

Since, all the angles of the vertices of the cyclic quadrilateral are 90

Thus, the cyclic quadrilateral is a rectangle.

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