Geometry · Cyclic quadrilaterals · Circle on a diameter · Parallelogram · Midline of a triangle · Inscribed angles
Let \(ABCD\) be a parallelogram whose interior angle at \(A\) is acute, and let \(E\) be a point of the plane such that \(EA \perp AB\) and \(EC \perp CB\). Prove that
\[ \angle AED = \angle CEB . \]
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Serbian Republic Competition (Republicko takmicenje) 2000, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source