1954 AHSME Problem 19

If the three points of contact of a circle inscribed in a triangle are joined, the angles of the resulting triangle:

\begin{array}{l} \textbf{(A)}\ \text{are always equal to }60^\circ\\ \textbf{(B)}\ \text{are always one obtuse angle and two unequal acute angles}\\ \textbf{(C)}\ \text{are always one obtuse angle and two equal acute angles}\\ \textbf{(D)}\ \text{are always acute angles}\\ \textbf{(E)}\ \text{are always unequal to each other} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.