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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.
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