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In triangle $ABC$, $AB=10$, $CA=12$. The bisector of ∠B intersects $CA$ at $E$, and the bisector of ∠C intersects $AB$ at $D$.

$AM$ and $AN$ are the perpendiculars to $CD$ and $BE$ respectively. If $MN=4$, then how can I find $BC$?

Thank you!

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    $\begingroup$ Whats your effort in this question. Did you tried it $\endgroup$ – Vedant Chourey May 14 at 12:14
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    $\begingroup$ math.stackexchange.com/questions/3221915/… $\endgroup$ – CY Aries May 14 at 13:20
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