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)` .

A straight line through the vertex P of a triangle P Q R intersects the side P Q at the point S and the circumcircle 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 S x S R)) 1/(P S)+1/(S T) 4/(Q R)

If p and q are true and r is false, then

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 .

O is the centre of the circle QOR is diameter. PQ is tangent to the circle. Given P hat(O)R = 130^(@) . Find O hat(P)Q .

Let P,Q,R and S be the feet of the perpendiculars drawn from point (1,1) upon the lines y=3x+4,y=-3x+6 and their angle bisectors respectively. Then equation of the circle whose extremities of a diameter are R and S is

Refer to the given figure and identify the parts labelled P,Q,R and S.

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is x^2+y^2=b^2 (b) x^2+y^2=a^2 x^2+y^2=a^2-b^2 (d) none of these

Find the value of a and b, given that p || q and r || s.