Three circles of equal radii have been drawn inside an equilateral triangle, of side a, such that each circle touches the other two circles as well as two sides of the triangle. Then, the radius of each circle is

Thirty-six equally spaced points - P1 through P36 - are plotted on a circle, and some of these points are joined successively to form a regular polygon. How many distinct such regular polygons are possible?

Which of the following is NOT a possible number of regions into which three straight lines (of infinite extent) can divide a plane?