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Perimeter inequality

Source: Indian TST 2019 Practice Test 1 P2

July 17, 2019
geometryperimeterinequalities

Problem Statement

Let ABCABC be a triangle with ∠A=∠C=30∘.\angle A=\angle C=30^{\circ}. Points D,E,FD,E,F are chosen on the sides AB,BC,CAAB,BC,CA respectively so that ∠BFD=∠BFE=60∘.\angle BFD=\angle BFE=60^{\circ}. Let pp and p1p_1 be the perimeters of the triangles ABCABC and DEFDEF, respectively. Prove that p≤2p1.p\le 2p_1.
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