**If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.**

**Solution:**

It is given that ABCD is a cyclic quadrilateral. Also, AC and BD are two diameters of circle having centre O.

We need to prove that ABCD is a rectangle.

BD is a diameter which means that **(1)**

**(Angle in a semi-circle is equal to )**

Similarly, AC is a diagonals which means that **(2)**

**(Angle in a semi-circle is equal to )**

From **(1)** and **(2)**, we can notice that opposite angles of quadrilateral ABCD are equal which makes it a parallelogram.

Also, all the corner angles are equal to which makes it a rectangle.