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 semicircle is

What whould be the work done, if a point charge .+q. is taken from a point A to a point B on the circumference of a circle drawn with another point charge +q at the centre?

What would be the work done if a point charge + q is taken from a point A to the point on the circumference of a circle with another point charge +q at the centre?

The normal at three points P, Q, R on a rectangular hyperbola intersect at a point T on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

If a point charge +q is taken first from A to C and then from C to B of a circle drawn with another point charge +q as centre as shown in the figure, then along which path more than will be done.

Let P Qa n dR S be tangent at the extremities of the diameter P R of a circle of radius rdot If P Sa n dR Q intersect at a point X on the circumference of the circle, then prove that 2r=sqrt(P Q x R S) .

Let RS be the diameter of the circle x^2+y^2=1, where S is the point (1,0) Let P be a variable point (other than R and S ) on the circle and tangents to the circle at S and P meet at the point Q.The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. then the locus of E passes through the point(s)-

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)

If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points are concyclic (i.e. lie on the same circle).

Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a . Let the line parallel to y-axis passing through P meet the circle x^2 +y^2=a^2 at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s and P varies over the ellipse.