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Relation in a convex quadrilateral formed from an acute triangle

Source: KAMO 2022 Grade 9 P2

July 5, 2022
geometryrectangle

Problem Statement

Let ABCABC be an acute triangle. Let DD be a point on the line parallel to ACAC that passes through BB, such that ∠BDC=2∠BAC\angle BDC = 2\angle BAC as well as such that ABDCABDC is a convex quadrilateral. Show that BD+DC=ACBD + DC = AC.
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