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← Okruzno takmicenje (Regional round) 2008Regional

Geometry · Circles · Parallel chords · Isosceles trapezoid · Common chord

Problem 1, 2008

RegionalProof

The circles \(k_1\) and \(k_2\) meet at two points \(A\) and \(B\). Through \(A\) and through \(B\) two parallel lines are drawn. They meet the circle \(k_1\) for a second time at the points \(C\) and \(D\), and the circle \(k_2\) for a second time at the points \(E\) and \(F\). Prove that \(CD = EF\).

A B C D E F k₁ k₂
One possible labelling: the line through \(A\) meets \(k_1\) again at \(D\) and \(k_2\) again at \(F\), the line through \(B\) meets \(k_1\) again at \(C\) and \(k_2\) again at \(E\).

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Serbian Regional Competition 2008, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source

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