Question 108
Let $a$, $b$ and $c$ be the side lengths of a triangle and suppose that $c^{2}=a^{2}+b^{2}+a b$. Which of the following statements holds 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 circumcircle of the triangle is the midpoint of the longest side.
(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 circumcircle of the triangle is the midpoint of the longest side.