If two triangles with side lengths $a,b,c$ and $a',b',c'$ and the corresponding angle $\alpha,\beta,\gamma$ and $\alpha',\beta',\gamma'$ satisfy $\alpha+\alpha'=\pi$ and $\beta=\beta'$, prove that $aa'=bb'+cc'$.
Source: Croatia MO 2002 2nd Grade P3
Tags: geometry, Triangles
If two triangles with side lengths $a,b,c$ and $a',b',c'$ and the corresponding angle $\alpha,\beta,\gamma$ and $\alpha',\beta',\gamma'$ satisfy $\alpha+\alpha'=\pi$ and $\beta=\beta'$, prove that $aa'=bb'+cc'$.