MathDB
Areas equation in a trapezoid

Source: V. Alekseev, V. Galkin, V. Panferov, V. Tarasov in Kvant 6/2000; re-used in 4th QEDMO as problem 2

November 10, 2007
geometrytrapezoidtrigonometry

Problem Statement

Let ABCD ABCD be a trapezoid with BC∥AD BC\parallel AD, and let O O be the point of intersection of its diagonals AC AC and BD 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.
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