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2s_1 <= s, semiperimeter inequality, incircle of 1 is circumcircle of other

Source: Indian Postal Coaching 2009 set 3 p4

May 26, 2020
geometrycircumcircleTrianglesperimeterGeometric Inequalities

Problem Statement

Let ABCABC be a triangle, and let DEFDEF be another triangle inscribed in the incircle of ABCABC. If ss and s1s_1 denote the semiperimeters of ABCABC and DEFDEF respectively, prove that 2s1≤s2s_1 \le s. When does equality hold?
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