In the adjacent figure, AB is a chord of circle with centre O. CD is the diameter perpendicualr to AB. Show that AD = BD

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

In the adjacent figure AB || CD. Find the value of x, y and z.

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.

AB is a chord of a circle with centre o and diameter 20 cm. If AB = 12 cm, find the distance of AB from O.

In the figure, O is the centre of the circle. Find the length of CD, if AB = 5 cm.

In the adjacent figure AB || CD. Find the values of x, y and z.

AB is a chord of a circle with centre O, AC is a diameter and AT is the tangent at A as shown in the figure. Prove that angleBAT=angleACB .

In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.

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.

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