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perpendiculars wanted, isosceles related (2015 HOMC Senior Q12)

Source:

July 19, 2019
geometryperpendicularisosceles

Problem Statement

Give an isosceles triangle ABCABC at AA. Draw ray CxCx being perpendicular to CA,BECA, BE perpendicular to CxCx (E∈CxE \in Cx).Let MM be the midpoint of BEBE, and DD be the intersection point of AMAM and CxCx. Prove that BD⊥BCBD \perp BC.
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