If is a rectangle and is any point inside of it, then we have
This can be proved by using the Pythagorean theorem and projecting point to the 4 sides of the rectangle.
Drop perpendicular lines from the point to the sides of the rectangle, meeting sides at points respectively, as shown in the figure. These four points form the vertices of an orthodiagonal quadrilateral. Applying the Pythagorean theorem to the right triangle and observing that it follows that
By a similar argument, the squared lengths of the distances from to the other three corners can be calculated as
(Source: MATHCOUNT 2014)
Point lies within rectangle . If , , and , what is
Let . By the British flag theorem, we have