Question 133
Let $ABC$ be an isosceles triangle with $|AC| = |BC|$. Its incircle touches $AB$ and $BC$ at $D$ and $E$, respectively. A line (different from $AE$) passes through $A$ and intersects the incircle at $F$ and $G$. The lines $EF$ and $EG$ intersect the line $AB$ at $K$ and $L$, respectively. Prove that $|DK| = |DL|$.