Geometry · Intersecting circles · Inscribed angle theorem · Equal chords and arcs · Congruent triangles
Circles \(k_1\) and \(k_2\) intersect at points \(P\) and \(Q\), and \(k_1\) passes through the centre of \(k_2\). Distinct points \(A\) and \(B\) lie on the arc of \(k_1\) that runs inside \(k_2\), and they are equidistant from the centre of \(k_2\). The line \(PA\) meets \(k_2\) at a point \(D \neq P\).
Prove that \(AD = PB\).
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Serbian Regional Competition (Okruzno takmicenje) 2015, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source