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construct K in acut ABC with <KBA = 2<KAB, <KBC = 2<KCB

Source: Sharygin Geometry Olympiad 2017 First Round P17 grades 9-11

July 22, 2018
geometryconstructionacute triangle

Problem Statement

Using a compass and a ruler, construct a point KK inside an acute-angled triangle ABCABC so that ∠KBA=2∠KAB\angle KBA = 2\angle KAB and ∠KBC=2∠KCB \angle KBC = 2\angle KCB.
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