Question

Prove that the perpendicular bisectors of the sides of a cycle quadrilateral are concurrent.

Answer 1

Let $ABCD$ be the cyclic quadrilateral.

Now, we know that perpendicular bisectors of chord passes through the centre of the circle.

Therefore, we can say that if $O$ is the centre of the circle then $OE,OF,EG$ and $OH$ are respectively the perpendicular bisectors of the cyclic quadrilateral $ABCD$, intersecting at the same point $O$.