Geometry · Circle on a diameter · Inscribed angles · Tangent lines · Circumcircle
Let \(ABC\) be an acute triangle. The circle \(k\) with diameter \(AB\) meets the side \(AC\) at \(M\) and the side \(BC\) at \(N\). The tangents to \(k\) at \(M\) and at \(N\) meet at the point \(P\). Given that \(CP = MN\), determine the angle \(\angle BCA\).
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Serbian Regional Competition 2010, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source