Question

if diagonals of cylic qadilateral are diameter of a circle through vertices of qadilateral ,then qadilateral is​

Answer 1

If diagonals of a cyclic quadrilateral are diameter of a circle through vertices of quadrilateral, then the quadrilateral is a rectangle.

Justification: Since it's diagonals are diameters, so we can say that the angle subtended by the semicircle so formed are right angles. You will observe that all angles are of 90°. So, the quadrilateral is a cyclic.

More:

Ptolemy’s theorem:-

“If in a quadrilateral, the product of it's vertices is equal to the product of two pair of it's opposite sides, then it is a cyclic.”

For e.g., let us take a cyclic □PQRS. Then,

PR × QS = PQ × RS = QR × PS.