Question

Two circles touch each other internally. the radius of the larger circle is 6 cm and the distance between the centre is 2 cm, then the radius (in cms) of the other circle is

Answer 1

draw a big circle and inside it draw a smaller circle touching the big one at point on circumference 
now assume the centres of the circle and then draw the radius of bigger one
passing through centre of the smaller one which touches its circumference at common point of the two circle and centre of big circle be o and that of smaller be o'
let radius of big circle be OA which is 6cm(GIVEN) and the distance between the centres OO' = 2cm(GIVEN)
as we can see that OA =OO' + O'A
                               6 =2 +O'A
                                4cm = O'A ,which is the radius of the smaller circle