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find OJ where J is symmetric of a right angle wrt I, related to R,r

Source: Sharygin 2010 Final 10.1

November 25, 2018
geometrycircumradiusinradiusMetric Relation

Problem Statement

Let O,IO, I be the circumcenter and the incenter of a right-angled triangle, R,rR, r be the radii of respective circles, JJ be the reflection of the vertex of the right angle in II. Find OJOJ.