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Isosceles triangle

Source: Balkan MO 2014 G-3

June 10, 2015
geometry

Problem Statement

Let △ABC\triangle ABC be an isosceles.(AB=AC)(AB=AC).Let DD and EE be two points on the side BCBC such that D∈BED\in BE,E∈DCE\in DC and 2∠DAE=∠BAC2\angle DAE = \angle BAC.Prove that we can construct a triangle XYZXYZ such that XY=BDXY=BD,YZ=DEYZ=DE and ZX=ECZX=EC.Find ∠BAC+∠YXZ\angle BAC + \angle YXZ.
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