Consider 8 vertices of a regular octagon and its centre. If T denotes the number of triangles and S denotes the number of straight lines that can be formed with these 9 points then the val of (T - S) =

If P denotes the perimeter and S denotes the sum of the distances of a point within a triangle from its angular points, then

T_m denotes the number of triangles that can be formed with the vertices of a regular polygon of m sides . If T_(m+1)- T_m=15 then m=

The number of triangle that can be formed by joining the vertices of a regular polygon of n sides is

If Delta denotes the area of any triangle and s its semiperimeter, prove that Delta is less than S^2/4

There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find , (i) the number of straight lines that can be obtained from the pairs of these points ? (ii) the number of triangles that can be formed for which the points are their vertices ?

There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, (i) the number of straight lines that can be obtained from the pairs of these points? (ii) the number of triangles that can be formed for which the points are their vertices?

There are 10 points in a plane, no three of which are in the same straight line, except 4 points, which are collinear. Find (i) the number of lines obtained from the pairs of these points, (ii) the number of triangles that can be formed with vertices as these points.

Let N denotes,the greatest number of points in which m straight lines and n circles intersect. Then,

Let N denotes,the greatest number of points in which m straight lines and n circles intersect. Then,