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ratio AC/DC is constant when <A=2<B

Source: 2022 Mathematics Regional Olympiad of Mexico West P4

October 6, 2022
ratiogeometryfixedequal angles

Problem Statement

Prove that in all triangles △ABC\vartriangle ABC with ∠A=2∠B\angle A = 2 \angle B it holds that, if DD is the foot of the perpendicular from CC to the perpendicular bisector of ABAB, ACDC\frac{AC}{DC} is constant for any value of ∠B\angle B.
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