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 $DK = DL$.
Školjka