## Realated Questions

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

If l+m+n=0, which of the following conditions must l, m and n satisfy so that the system of simultaneous linear equations x+3y-4z=l, 2x-y-z=m, x+y-2z=n has at least one ?

Thirty-six equally spaced points - P

_{1}through P_{36}- 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?