Geometry · Rectangles · Congruent triangles · Right triangle median · Intercept theorem
Let \(K\) be the midpoint of the side \(CD\) of a rectangle \(ABCD\). The lines \(BK\) and \(AC\) are perpendicular to each other and meet at the point \(H\), and \(G\) denotes the foot of the perpendicular dropped from \(D\) to \(AC\). Prove that
a) \(\angle ACB = \angle DHA\);
b) \(GH = \tfrac{1}{3}AC\).
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Serbian Municipal Competition 2018, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source