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MathNet 2025 — 50 problems with figures (EN–VI) Question 42

Math Olympiad Vault · MathNet 2025 — 50 problems with figures (EN–VI)

Question 42

The isosceles triangle $ABC$ has $\angle BAC = 30^\circ$ and $AB = AC$. Take the point $D$ on the side $AC$ and the distinct points $E$, $F$, $G$ on the side $AB$ so that $BC = BD = DE = EF$ and $DG = DF$.

a) Prove that $BF = GE$.

b) Find the measure of $\angle BCG$.

Question illustration