1993 AHSME Problems/Problem 25

Problem

$[asy] draw(circle((0,0),10),black+linewidth(.75)); MP(")",(0,0),S); [/asy]$

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

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

Solution

$\fbox{E}$

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 2
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1993 AHSME Problems/Problem 25

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