# Cemicirlces

Author: mathforces
Problem has been solved: 16 times

Русский язык | English Language

In the triangle $XYZ$ it is given that $XY=15$, $YZ=12$, $ZX=9$. Let $x$, $y$ and $z$ - cemircles with diameters $YZ$, $ZX$ and $XY$ respectively, erected externally with respect to the triangle. Points $L$, $M$ and $N$ are chosen on $x$, $y$ и $z$ respectively such that $\angle ZYL=\angle XZM=\angle YXN=15^{\circ}$. Area of the triangle $LMN$ can be represented as an irreduciable fraction $\frac{a}{b}$, where $a$ и $b$ are positive integer numbers. Find $a-b$.