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converse of perpendicularity in isosceles triangle (ASU 1962)

Source: China Northern MO 2014 p1 CNMO

October 29, 2022
geometryperpendicularisosceles

Problem Statement

As shown in the figure, given △ABC\vartriangle ABC with ∠B\angle B, ∠C\angle C acute angles, AD⊥BCAD \perp BC, DE⊥ACDE \perp AC, MM midpoint of DEDE, AM⊥BEAM \perp BE. Prove that △ABC\vartriangle ABC is isosceles. https://cdn.artofproblemsolving.com/attachments/a/8/f553c33557979f6f7b799935c3bde743edcc3c.png
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