In the adjacent figure, there are two concentric circles with centre ‘O’. Chord AD of the bigger circle intersects the smaller circle at B and C. Show that AB = CD.

In the given figure, there are two circles with centers A and B. The common tangent to the circles touches them, respectively,at P and Q. AR is 40cm and AB is divided by the point of contact of the circles in the ratio 5:3 The length of QR is

Two concentric circles of radii 5cm and 3cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.

Chords AB and CD of a circle intersect inside the circle at point E . If AE = 5.6, EB = 10, CE = 8,find ED.

In the adjoining figure circles with centres A and C touch internally at point T . Line AB is tangent to the smaller circle at point P . Point B lies on the bigger circle. Radii are 16 cm and 6 cm . Find AP.

In the adjoining figure,seg AB is a diameter of a circle with centre O . Bisector of inscribed angleACB intersects circle at point D. Complete the following proof by filling in the blanks. Prove that : seg AD ~= seg BD

In figure if PR is tangent to the circle at P and O is the centre of the circle then angle POQ is

In the adjoining figure seg RS is the dianeter of the circle with centre 'O' . Point T is in the exterior of the circle . Prove that angleRTS is an acute angle.

In the adjoining figure, two circles intersect each other at points A and E . Their common secant through E intersects the circle at points B and D . The tangents of the circles at point B and D intersect each other at point C . Prove that squareABCD is cyclic .