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isosceles criterion, equal perpσ on bisectors (Ukr. Geom. Olympiad '20 VIII p1)

Source:

June 8, 2020
geometryisoscelesangle bisectorperpendicular

Problem Statement

In triangle ABCABC, bisectors are drawn AA1AA_1 and CC1CC_1. Prove that if the length of the perpendiculars drawn from the vertex BB on lines AA1AA1 and CC1CC_1 are equal, then △ABC\vartriangle ABC is isosceles.
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