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TOT 280 1990 Autumn A S5 exradius wanted starting with isosceles

Source:

June 8, 2024
exradiusgeometry

Problem Statement

In triangle ABCABC we have AC=CBAC = CB. On side ABAB is a point DD such that the radius of the incircle of triangle ACDACD is equal to the radius of the circle tangent to the segment DBDB and to the extensions of the lines CDCD and CBCB. Prove that this radius equals a quarter of either of the two equal altitudes of triangle ABCABC.
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