$17 \cdot 8$ In a right triangle, when the square of the hypotenuse is equal to twice the product of the two legs, then one of the acute angles of the triangle is
(A) $15^{\circ}$.
(B) $30^{\circ}$.
(C) $45^{\circ}$.
(D) $60^{\circ}$.
(E) $75^{\circ}$.
(10th American High School Mathematics Examination, 1959)
[Solution] Let the three sides of the right-angled triangle be $a, b, c$. According to the problem and the Pythagorean theorem, we have:
$$
c^{2}=2 a b, \quad c^{2}=a^{2}+b^{2},
$$

Thus, $a^{2}+b^{2}=2 a b$, which leads to $a=b$.

Therefore, the answer is $(C)$.