Let

be an isosceles triangle with

. Its incircle touches

in

and

in

. A line distinct of

goes through

and intersects the incircle in

and

. Line

intersects line

and

in

and

, respectively. Prove that

.
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Let $ABC$ be an isosceles triangle with $AC = BC$. Its incircle touches $AB$ in $D$ and $BC$ in $E$. A line distinct of $AE$ goes through $A$ and intersects the incircle in $F$ and $G$. Line $AB$ intersects line $EF$ and $EG$ in $K$ and $L$, respectively. Prove that $DK = DL$.