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← Okruzno takmicenje (Regional round) 2022Regional

Geometry · Ruler and compass construction · Thales circle · Inscribed angles · Brocard point

Problem 3, 2022

RegionalProof

Let \(ABC\) be a right triangle. Construct a point \(N\) inside \(\triangle ABC\) for which

\[ \angle NBC = \angle NCA = \angle NAB. \]
A B C N φ φ φ
The three marked angles must be equal. The point \(N\) is what has to be constructed.

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Serbian Regional Competition (Okruzno takmicenje) 2022, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source

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