AB and CD are two diameters of a circle. Prove that ADBC is a rectangle

AB and CD are two diameters of a circle 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 adjoining figure, O is the centre of a circle in which AB and CD are two diameters. Prove that AC|\ |BD and AD|\ |BC . If angleOBD =50^@ , then find the value of angleAOC .

In the adjoining figure, O is the centre of a circle in which AB and CD are two diameters. Prove that AC|\ |BD and AD|\ |BC . If angleOBD =50^@ , then find the value of angleAOC .

AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and AB is parallel to CD. The distance between AB and CD is 3 cm. Find the radius of the circle.

AB and CD are two chords of a circle such that AB = 10 cm, CD - 24 cm and AB||CD. If the distance between AB and CD is 17 cm. Then, the radius of the circle is equal to