Junior Balkan MO 2004 - Problem 2


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27. listopada 2023.
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Let ABC be an isosceles triangle with |AC|=|BC|, let M be the midpoint of its side \overline{AC}, and let Z be the line through C perpendicular to \overline{AB}. The circle through the points B, C, and M intersects the line Z at the points C and Q. Find the radius of the circumcircle of the triangle ABC in terms of m = |CQ|.

Izvor: Juniorska balkanska matematička olimpijada 2004.