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midpoint of segment in a triangle 75-60-45

Source: BMO SL 2019, G2

November 8, 2020
geometry

Problem Statement

Let be a triangle △ABC\triangle ABC with m(∠ABC)=75∘m(\angle ABC) = 75^{\circ} and m(∠ACB)=45∘m(\angle ACB) = 45^{\circ}. The angle bisector of ∠CAB\angle CAB intersects CBCB at point DD. We consider the point E∈(AB)E \in (AB), such that DE=DCDE = DC. Let PP be the intersection of lines ADAD and CECE. Prove that PP is the midpoint of segment ADAD.
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