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MathNet 2025-part-02 — 186 problems (EN–VI) Question 60

Math Olympiad Vault · MathNet 2025-part-02 — 186 problems (EN–VI)

Question 60

Let $ABC$ be a triangle with $AB = 2AC$. Let $D$ be the midpoint of side $AB$. A point $E$ is chosen on side $BC$ such that $\angle BDE = \angle ACB$.

a) Show that the ray ($EA$ bisects angle $\angle CED$.

b) Let $O$ be the intersection of lines $CD$ and $AE$. Show that $\angle COA = \angle ACB$.