Example 3. If the three sides of a triangle are $a, b, c$, and the three interior angles are $A, B, C$, and they satisfy $a \cos A + b \cos B = c \cos C$, then this triangle must be
(A) an equilateral triangle; (B) a right triangle with $a$ as the hypotenuse; (C) a right triangle with $b$ as the hypotenuse; (D) none of the above (A), (B), (C).
Since the edge-angle relationship given in the problem is symmetric with respect to $a, b$, and the answer is unique, options $(B), (C)$ should be excluded simultaneously. Also, when $a=b=c$, the given equation obviously does not hold, so option $(A)$ should also be excluded. Therefore, the answer is $(D)$.