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← Okruzno takmicenje (Regional round) 2010Regional

Geometry · Circle on a diameter · Inscribed angles · Tangent lines · Circumcircle

Problem 3, 2010

RegionalOpen answer

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 \(\angle BCA\).

ABC MNP k
A sketch of the configuration for a general acute triangle; the hypothesis \(CP = MN\) is not drawn to scale.

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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

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