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Find the circumradius of triangle

Source: Sharygin contest. The final raund. 2008. Grade 9. Second day. Problem 7

August 31, 2008
geometrycircumcircleparallelogramgeometric transformationreflectiongeometry unsolved

Problem Statement

(A.Zaslavsky) The circumradius of triangle ABC ABC is equal to R R. Another circle with the same radius passes through the orthocenter H H of this triangle and intersect its circumcirle in points X X, Y Y. Point Z Z is the fourth vertex of parallelogram CXZY CXZY. Find the circumradius of triangle ABZ ABZ.
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