A2. Let $a, b$ and $c$ be the lengths of the sides of a triangle, and let $c^{2}=a^{2}+b^{2}+a b$. Which of the following statements is true for such a triangle?
(A) The triangle is equilateral.
(B) The triangle is acute.
(C) The orthocenter lies outside the triangle.
(D) The triangle is right-angled.
(E) The center of the circumscribed circle of the triangle is the midpoint of the longest side.
A2. From the cosine rule $c^{2}=a^{2}+b^{2}-2 a b \cos \gamma$ and the equation $c^{2}=a^{2}+b^{2}+a b$ we get $a b=-2 a b \cos \gamma$. From this, it follows that $\cos \gamma=-\frac{1}{2}$ or $\gamma=120^{\circ}$. The triangle is obtuse, so the orthocenter lies outside the triangle.