If three points P, Q, R are taken at random on the circumference of a circle, the chance that do not lie on the same samicircle is

Points A (-1, y) and B (5, 7) lie on the circumference of a circle with centre O (2,-3y). Find y. Hence find the radius of the circle.

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals:

Three persons P, Q, R are at the three comers of an equilateral triangle of each side 1. They start moving simultaneously with velocity v such that Pathways moves towards Q Q always moves towards R and R always moves towards P. After what time they would meet each other at O?

Consider the two 'postulates' gives below: (i) Given any two distinct points A and B, there exists a third point C, which is between A and B. (ii) There exist at least three points that are not on the same line. Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid's postulates? Explain.

In the figure, PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that |__SQL=50^(@) and |__SRM=60^(@) . Find |__QSR .

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 :

Statement-1: There are pge8 points in space no four of which are in the same with exception of q ge3 points which are in the same plane, then the number of planes each containing three points is .^(p)C_(3)-.^(q)C_(3) . Statement-2: 3 non-collinear points always determine unique plane.

Consider the two 'Postulates' given below. (ii) There exists at least three points that are not on the same line Do these postulates contain any undefined terms ? Do they follow from Euclid's postulates ? Explain.