Pythagorean Theorem (direct and inverse). Area of a quadrilateral

A quadrilateral is inscribed in a circle of radius 13, with diagonals that are perpendicular to each other. One of the diagonals is 18, and the distance from the center of the circle to the point of intersection of the diagonals is \(4 \sqrt{6}\).

Find the area of the quadrilateral.
The area of such a quadrilateral is equal to half the product of its diagonals.

## Answer

$18 \sqrt{161}$.