Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to `1/3` of the larger part. Then find the length of the larger part.

Split 69 in three parts such that they are in A.P and product of two smaller parts is 483 . Find the three parts.

If a magnet of pole strenth m is divided into four parts such that the length and width of each part is half that of initial one, then the pole strength of each part will be

Divide 207 in three parts, such that all parts are in A.P and product of two smaller parts is 4623 .

A wire of length l is cut in to two parts. One part is bent into a circle and the other into a square. Show that the sum of the areas of the circle and the square is least, if the radius of the circle is half the side of the square.

If radius of a circle is 4.3 cm, then find length of longest chord.

Find the length of the longest chord of the circle of radius 5.2 cm.

A circle of radius 2 cm touches a circle of radius 10cm internally. Determine the length of a tangent segment drawn through the cente of the larger circle to the smaller circle.