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 P Q and R S be tangent at the extremities of the diameter P R of a circle of radius r . If P S and R Q intersect at a point X on the circumference of the circle, then prove that 2r=sqrt(P Q xx R S) .

Let PQ and RS be tangents at the extremities of one diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, than (2r)/sqrt(PQ cdot RS) equals_____

The tangents are drawn at the extremities of diameter AB of a circle with centre P. If a tangent to the circle at the point C intersects the other two tangents at Q and R, thenthe measure of the angleQPR is___

A point P is given on the circumference of a circle of radius r. The chord QR is parallel to the tangent line at P. Find the maximum area of the triangle PQR.

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST

If S be the sum, P the product and R the sum of the reciprocal of n terms in G.P., prove that, p^(2) = ((S)/(R ))^(n) .

Two circles intersect each other at the points P and Q. Two straight lines through P and Q intersect on circle at the points A and C and the other circle at B and D . Prove that AC||BD.

The internal and external bisectors of the vertical angle of a triangle intersect the circumcircle of the triangle at the points P and Q. Prove that PQ is a diameter of the circle.

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