A straight line intersects thethree concentric circles at A, B, C. if the distance of line from the centre of the circles is 'P', prove that the area of the triangle formed by tangents to the circle at A, B, C is `((1)/(2P).AB.BC.CA)`.

If a line intersects two concenteric circles (circles with the same centre) with center O at A,B,C and D, prove that AB=CD (see figure).

If a , b , c are in G.P. write the area of the triangle formed by the line a x+b y+c=0 with the coordinates axes.

In the figure, two circles intersect at A and B . A C and A D are respectively the diameters of the circles. Prove that C , B , D are collinear.

In Figure, l is a line intersecting the two concentric circles, whose common centre is O , at the points A ,B ,C and D . Show that A B=C Ddot

The extremities of a diagonal of a rectangle are (-4, 4) and (6, -1) . A circle circumscribes the rectangle and cuts an intercept AB on the y-axis. If Delta be the area of the triangle formed by AB and the tangents to the circle at A and B , then 8Delta = .

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

The circle above with centre A has an area of 21. BC is tangent to the circle with centre A at point B. IF AC=2AB, then what is the area of the shaded region?

The straight line x-2y+5=0 intersects the circle x^(2)+y^(2)=25 in points P and Q, the coordinates of the point of the intersection of tangents drawn at P and Q to the circle is

A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line, then the locus of centre of the circle is :