Two circles cut at A and B and a straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersects at R, prove that R,P,B,Q are concyclic.

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangents at P and Q intersect at point T, show that the points P, B, Q and T are concylic.

Two equal circles intersect in P and Q.A straight line through P meets the circles in A and B. Prove that QA=QB

Two equal circles intersect in P and Q . A straight line through P meets the circles in A and B . Prove that Q A=Q Bdot

Two equal circles intersect in P and Q . A straight line through P meets the circles in A and B . Prove that Q A=Q Bdot

Two circles intersects in points P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that the A,Q,B and T lie on a circle.

ABCD is a parallelogram. The circle through A,B is so drawn that it intersects AD at P and CB at Q. Prove that P,Q,C and D are concyclic.

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Consider the circle x^2+y^2=9 and the parabola y^2=8x . They intersect at P and Q in the first and fourth quadrants, respectively. Tangents to the circle at P and Q intersect the X-axis at R and tangents to the parabola at P and Q intersect the X-axis at S. The ratio of the areas of trianglePQS" and "trianglePQR 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-