20.41 Connecting the three points of tangency of the incircle of a triangle, the angles of the resulting triangle
(A) are all equal to $60^{\circ}$.
(B) one obtuse angle and two unequal acute angles.
(C) one obtuse angle and two equal acute angles.
(D) are all acute.
(E) are unequal to each other.
(5th American High School Mathematics Examination, 1954)
[Solution] Using the property of the angle of tangency, we can easily obtain:
$$
\begin{aligned}
\angle A & =180^{\circ}-2 \angle B^{\prime} \\
& =180^{\circ}-2 \angle A^{\prime},
\end{aligned}
$$

Thus, $2 \angle A^{\prime}=180^{\circ}-\angle A$,
which gives $\angle A^{\prime}=90^{\circ}-\frac{1}{2} \angle A<90^{\circ}$.
Similarly, we can prove $\angle B^{\prime}<90^{\circ}, \angle C^{\prime}<90^{\circ}$.
Therefore, $\triangle A^{\prime} B^{\prime} C^{\prime}$ is an acute triangle.
Hence, the answer is $(D)$.