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)` .

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

True/False: Let O be the centre of a circle with radius r. Then a point P such that OP < r is called an interior point of the circle.

AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, prove that 4q^2 = p^2 + 3r^2

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 the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S. The radius of the circumcircle of the triangle PRS is-

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P^2R^n = S^n .

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P^(2)R^(n) = S^(n) .

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)-

Tangents PQ, PR are drawn to the circle x^(2)+y^(2)=36 from the point p(-8,2) touching the circle at Q,R respectively. Find the equation of the circumcircle of DeltaPQR .