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double segment given, double angle wanted, around intesecting circles

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P5

August 2, 2018
geometryanglescircles

Problem Statement

Let a triangle ABCABC be given. Two circles passing through AA touch BCBC at points BB and CC respectively. Let DD be the second common point of these circles (AA is closer to BCBC than DD). It is known that BC=2BDBC = 2BD. Prove that ∠DAB=2∠ADB.\angle DAB = 2\angle ADB.
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