Draw different pairs of circles. How many points does each pair have in common ? What is the maximum number of common points ?

There are three coplanar lines. If any p points are taken on each of the lines , the maximum number of triangles with vertices at these points is :

A person tries to form as many different parties as he can, out of his 20 friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?

The maximum number of points of intersection of 7 circles is

Two circles intersect each other. Then the total number of common tangents that can be drawn to them is :

Let ngeq2 be integer. Take n distinct points on a circle and join each pair of points by a line segment. Color the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

Draw a circle the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.