Geometry · Cyclic quadrilaterals · Orthogonal projections · Chords and midpoints · Thales theorem
The quadrilateral \(ABCD\) is inscribed in a circle, and its diagonal \(AC\) is a diameter of that circle. Prove that the projections of the sides \(AB\) and \(CD\) onto the diagonal \(BD\) are equal.
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Serbian Municipal Competition 2003, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source