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← Drzavno takmicenje (National round) 2008National

Geometry · Napoleon triangle · Constant angle locus · Circumscribed triangles · Composition of rotations · Chord midpoints · Extremal construction

Problem 4, 2008

NationalProof

Circumscribe about a given triangle \(ABC\) an equilateral triangle \(PQR\) whose side is as long as possible.

(Here \(\triangle PQR\) is called circumscribed about \(\triangle ABC\) when \(A \in QR\), \(B \in RP\) and \(C \in PQ\).)

A B C P Q R
One equilateral triangle circumscribed about \(ABC\). There are infinitely many; the problem asks for the biggest.

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Serbian National Competition (Drzavno takmicenje) 2008, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source

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