1993 AHSME Problem 25

Let S be the set of points on the rays forming the sides of a 120^{\circ} angle, and let P be a fixed point inside the angle on the angle bisector. Consider all distinct equilateral triangles PQR with Q and R in S. (Points Q and R may be on the same ray, and switching the names of Q and R does not create a distinct triangle.) There are

\begin{array}{l} \text{(A) exactly 2 such triangles} \quad\\ \text{(B) exactly 3 such triangles} \quad\\ \text{(C) exactly 7 such triangles} \quad\\ \text{(D) exactly 15 such triangles} \quad\\ \text{(E) more than 15 such triangles} \end{array}

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