MathNet 2008-part-03 — 165 problems (EN–VI) Question 59

In a circle with diameter $d$ the chords $AB$ and $CD$ are perpendicular and intersect at a point $E$ distinct from the centre of the circle. Prove that $\overline{AE}^2 + \overline{BE}^2 + \overline{CE}^2 + \overline{DE}^2 = d^2$.