MathNet 2025-part-01 — 187 problems (EN–VI) Question 109

Let $\triangle ABC$ be an isosceles triangle with $AC = BC$. Points $D$ and $E$ are placed on sides $AC$ and $AB$, respectively. Let segments $EC$ and $BD$ intersect at point $G$. If the area of quadrilateral $ADGE$ is equal to that of triangle $BGC$, and if $EC = BD$, prove that $\angle EGB = \angle ACB$.

(Khulan Tumenbayar)