A2. For the lengths $a, b$, and $c$ of the sides of triangle $ABC$, it holds that $c^{2}=2 a b$ and $a^{2}+c^{2}=3 b^{2}$. The measures of the interior angles of triangle $ABC$ are
(A) $30^{\circ}, 60^{\circ}$, and $90^{\circ}$.
(B) $45^{\circ}, 60^{\circ}$, and $75^{\circ}$.
(C) $45^{\circ}, 45^{\circ}$, and $90^{\circ}$.
(D) $60^{\circ}, 60^{\circ}$, and $60^{\circ}$.
(E) It is impossible to determine.