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calculate the circumradius

Source: 2012 Sharygin Geometry Olympiad Final Round 9.6

August 3, 2018
geometrycircumcircleisosceles

Problem Statement

Let ABCABC be an isosceles triangle with BC=aBC = a and AB=AC=bAB = AC = b. Segment ACAC is the base of an isosceles triangle ADCADC with AD=DC=aAD = DC = a such that points DD and BB share the opposite sides of AC. Let CMCM and CNCN be the bisectors in triangles ABCABC and ADCADC respectively. Determine the circumradius of triangle CMNCMN.
(M.Rozhkova)
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