Prove that any three points on a circle cannot be collinear.

There are n points in a plane. Find the number of straight lines that can be obtained by joining points if a) no three points are collinear. b) p points are collinear.

In the adjoining figure, A,B and C are three points on a circle with centre O such that mangleAOB=110^@ , mangleAOC=120^@ . Find mangleBAC .

Find the number of triangles formed by joining 12 points if a) no three points are collinear b) four points are collinear.

Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.

Prove that any rectangle is a cyclic quadrilateral.

If the position vectors of the points A,B,C are bara,barb and 3bara-2barb respectively, then the points A,B,C are: a)Collinear b)Non-collinear c)Forming a right angled triangle d)None of these

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.