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Comparing inradii of triangles

Source: India TST 2016 Day 4 Problem 1

July 22, 2016
geometryinradiuscircumcircleinequalitiesgeometric inequality

Problem Statement

Let ABCABC be an acute triangle with circumcircle Γ\Gamma. Let A1,B1A_1,B_1 and C1C_1 be respectively the midpoints of the arcs BAC,CBABAC,CBA and ACBACB of Γ\Gamma. Show that the inradius of triangle A1B1C1A_1B_1C_1 is not less than the inradius of triangle ABCABC.
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