Question

if diagonals of cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral prove that it is rectangle ​

Answer 1

let the quadrilateral be ABCD

in quadrilateral ,

angleA = angle C

in cyclic quadrilateral

angleA+angleC= 180

angleA+angleA=180

2angleA=180

angleA=180/2

angleA=90°

so this a rectangle

because in rectangle one of its angle is right angle