#24

Let $P$ be an interior point of a triangle $ABC$ whose side lengths are $26,65,78$ .The line through $P$ parallel to $BC$ meets $AB$ in $K$ and $AC$ in $L$ .The line through $P$ parallel to $CA$ meets $BC$ in $M$ and $BA$ in $M$ .The line through $P$ parallel to $AB$ meets $CA$ in $S$ and $CB$ in $T$ .If $KL$ , $MN$ , $ST$ are of equal lengths,find this common length.

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$