<p>This is one of the two problems i got on a paper.It is from a Kaplan test booklet. Please help me out guys.</p>
<p>A circle and a triangle are drawn on a piece of paper. Which of the following is the set of the number of possible points that are common to both the circle and the triangle?</p>
<p>(A) ----> (0,2)
(B) ----> (0,1,2,3)
(C) ----> (2,4,6)
(D) ----> (1,2,3,4,5,6)
(E) ----> (0,1,2,3,4,5,6)</p>
<p>Is the answer E?</p>
<p>Yes the answer is (E). It is easy to draw all 7 possibilities.</p>
<p>For example, for 0 just draw a small triangle and then a large circle around it (so that the triangle is inside the circle and doesn’t touch it).</p>
<p>As another example, for 3 draw a triangle inscribed in a circle.</p>
<p>For 6, draw a circle, and then have each side of the triangle intersect the circle twice.</p>
<p>Etc…</p>
<p>Circle tangent to the triangle at some point: +1 intersection
Circle intersects a side length of the triangle at two points: +2 intersections</p>
<p>This enables you to have anywhere from 0 to 6 intersections inclusive.</p>