Question 61
On the sides $AB$ and $AC$ of triangle $ABC$ the triangles $AEB$ and $ADC$ are constructed, both similar to $\triangle ABC$ and with $\angle AEB = \angle ADC = \angle BAC$. Prove that the area of $\triangle ABC$ is less than, equal to or greater than the sum of the areas of triangles $AEB$ and $ADC$ according as $\angle BAC$ is less than, equal to or greater than a right angle.