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The figure below shows an isosceles triangle ABC (AB = BC) with the altitude BH and a cevian BD. O_{1} and O_{2} are the incircles of triangles ABD and BDC. If E and F are the tangency points, prove that EH = DF.

See also: Kaleidoscope of Problem 1149 base on Poincare Disk Model. Isolines of problem 1149.

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