Geometric properties of a circle
Consider the first picture, suppose the quadilateral as shown, with one vertex at the centre of the circle. Then we all know that the angle at the centre is twice the angle at the top vertex. Now suppose we have a quadilateral as shown in the second picture. How can we prove the converse? i.e. there exists a circle such that 3 of the corners cut the circle, and the centre of the circle coincides with the remaining vertex?