Geometry · Congruent circles · Rhombus · Inscribed angle theorem · Johnson circles · Concurrent circles
Congruent circles \(k_1\), \(k_2\) and \(k\) all pass through a point \(P\), and each pair of them meets in one further point: \(k\) and \(k_1\) meet again at \(A\), \(k\) and \(k_2\) meet again at \(B\), and \(k_1\) and \(k_2\) meet again at \(N\). Let \(k_A\) be the circle with centre \(A\) passing through \(N\), and let \(k_B\) be the circle with centre \(B\) passing through \(N\). Prove that \(k_A\), \(k_B\) and \(k\) have a common point.
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Serbian Regional Competition (Okruzno takmicenje) 2013, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source