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right ABC, altitiude BH, relation between 3 inradii wanted

Source: Mexican Mathematical Olympiad 1990 OMM P2

July 29, 2018
geometryright triangleinradius

Problem Statement

ABCABC is a triangle with ∠B=90o\angle B = 90^o and altitude BHBH. The inradii of ABC,ABH,CBHABC, ABH, CBH are r,r1,r2r, r_1, r_2. Find a relation between them.
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