Find product of radii of two circles whose length of common internal tangent is 7 and that of common external tangent is 11.

The length of common external tangent is 11 units. We can draw it as follows :

Let dbe the distance of the centres of the circle. Let abe the radius of large circle and bbe the radius of smaller circle.

From O', draw a line parallel to AB which meets OA and C.

In Right angled ΔOCO', we have –

Again, the length of common internal tangent to these two circles is 7 units. We can draw it as –

Here PQ = 7 units is the length of common internal tangent.

Draw a line O'R parallel to PQ so that it makes a right angled triangle OO'R with

OR = OP + PR =a+bunits

O'R = PQ = 7 units

and OO' =dunits

By Pythagoras theorem,

subtracting (2) from (1) we get –

Hence the product of radius of two circles is 18 square units.