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Angle and bisection (Simple)

Source: Greek National MO 2015

March 4, 2015
geometry

Problem Statement

Given is a triangle ABCABC with ∠B=105∘\angle{B}=105^{\circ}.Let DD be a point on BCBC such that ∠BDA=45∘\angle{BDA}=45^{\circ}.
A) If DD is the midpoint of BCBC then prove that ∠C=30∘\angle{C}=30^{\circ}, B) If ∠C=30∘\angle{C}=30^{\circ} then prove that DD is the midpoint of BCBC
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