Geometry · Circumcenter · Cyclic quadrilaterals · Inscribed angle · Angle bisector
In a triangle \(ABC\) the bisector of the angle at the vertex \(A\) meets the side \(BC\) at the point \(D\). The perpendicular dropped from \(B\) to the line \(AD\) meets the circumcircle of the triangle \(ABD\) at a point \(E \neq B\).
Prove that the centre \(O\) of the circumcircle of the triangle \(ABC\) lies on the line \(AE\).
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Serbian Regional Competition 2014, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source