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 `

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.

A line intersecting a circle in two points is called a secant.

As shown in the figure, AB and CD are two common tangents to circles with centres O_(1) and O_(2) and different radius. Prove that AB=CD

AB and CD are respectively arcs to two concentric circles of radii 21cm and 7cm with centre O ( See figure), If /_AOB=30^(@) , find the area of the shaded region. (usepi=(22)/(7))

In the given figure, two concentric circles with centre O and radii 5cm and 3 cm are given, PA and PB are tangents to those circle at A and B respectively. If PA =12cm, find PB.

Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and angle AOC = 40^(@) .

Two tangent segments PA and PB are drawn to a circle with centre O such that angleAPB=120^@ . Prove that OP=2AP.

AB is a diameter and AC is a chord of a circle with centre O such that angleBAC=30^@ . The tangent at C intersects AB at a point D. Prove that BC=BD.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.