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Part of 2001 Czech And Slovak Olympiad IIIA

Problems(1)

right triangle construction

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2001 p2

2/11/2020
Given a triangle PQXPQX in the plane, with PQ=3,PX=2.6PQ = 3, PX = 2.6 and QX=3.8QX = 3.8. Construct a right-angled triangle ABCABC such that the incircle of △ABC\vartriangle ABC touches ABAB at PP and BCBC at QQ, and point XX lies on the line ACAC.
geometric constructionconstructionright trianglegeometryincircle