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 concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD

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

Find the locus of the centre of a circle which passes through the origin and cuts off a length 2b from the line x=c .

Two cocentric circle common centre O. A line 'l' intersects these circle A,B,C and D. Prove that AB = CD.

Two circles intersect at A and and AC,AD are respectively the diameter of the circle . Prove that the points C,B and D are collinear.

ABCD is such a quadrilateral A is the centre of the circle passing through B,C and D. Prove that : angleCBD + angleCDB = 1/2 angleBAD

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

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chord.

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

In fig., two circles with centres O, O' touch externally at a point A. A line through A is drawn to intersect these circles in B and C. Prove that the tangents at B and C are parallel.