Geometry · Isosceles triangles · Thales circle · Auxiliary rectangle · Inscribed angles · Parallelograms · Similar triangles
Let \(ABC\) be an isosceles triangle with \(AB = AC\). Let \(D\) be the point of the side \(AC\) for which \(CD = 2 \, AD\), and let \(P\) be a point of the segment \(BD\) with \(\angle APC = 90^\circ\). Prove that
\[ \angle ABP = \angle PCB . \]
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Serbian Republic Competition (Republicko takmicenje) 2005, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source