In the figure, two circles touch internally at point P. chord AB of the larger circle intersects the smaller circle in C and D. Prove `/_CPA cong /_DPB`.

In the adjoining figure, O is the centre of two concentric circles. The chord AB of larger circle intersects the smaller circle at C and D. (i) Find AC:BD . (ii) If AC=2cm , then find the length of BD.

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA cong"arc "PYB .

In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that: (i) tangent at point P bisects AB (ii) angle APB=90^(@)

The adjoining figure shows two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm.Find: (a) the area of the larger circle (b) the area of the smaller circle (c) the shaded area between two circles ( π=3.14)

The figure shows two concentric circles and AD is a chord of larger circle. Prove that : AB = CD.

Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

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 the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

In the given figure two small circles touch each other externally at the centre of a big circle and these small circles are touched internally by a big circle of radius 4cm. Find the area of the shaded region

In two concentric circle, prove that a chord of larger circle which is tangent to smaller circle is bisected at the point of contact.