<imgclass="img-responsive center-block"alt="triangle ABC, with angular bisectors intersecting sides at the points E, F and G"src="https://cdn.freecodecamp.org/curriculum/project-euler/angular-bisectors.gif"style="background-color: white; padding: 10px;">
The segments $EF$, $EG$ and $FG$ partition the triangle $ABC$ into four smaller triangles: $AEG$, $BFE$, $CGF$ and $EFG$. It can be proven that for each of these four triangles the ratio $\frac{\text{area}(ABC)}{\text{area}(\text{subtriangle})}$ is rational. However, there exist triangles for which some or all of these ratios are integral.