Let ABCD be a trapezoid with BC∥AD, and let O be the point of intersection of its diagonals AC and BD. Prove that \left\vert ABCD\right\vert \equal{}\left( \sqrt{\left\vert BOC\right\vert }\plus{}\sqrt{\left\vert DOA\right\vert }\right) ^{2}.
[hide="Source of the problem"]Source of the problem: exercise 8 in: V. Alekseev, V. Galkin, V. Panferov, V. Tarasov, Zadachi o trapezijah, Kvant 6/2000, pages 37-4. geometrytrapezoidtrigonometry