Let S be the set of points on the rays forming the sides of a 120∘ 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
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draw((0,0)--(6,10.2), EndArrow);
draw((0,0)--(6,-10.2), EndArrow);
draw((0,0)--(6,0), dotted);
dot((6,0));
label("P", (6,0), S);
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<spanclass=′latex−bold′>(A)</span>exactly 2 such triangles<spanclass=′latex−bold′>(B)</span>exactly 3 such triangles<spanclass=′latex−bold′>(C)</span>exactly 7 such triangles<spanclass=′latex−bold′>(D)</span>exactly 15 such triangles<spanclass=′latex−bold′>(E)</span>more than 15 such triangles