Some more Tangent Circles.
Given three circles which share the same tangent and touch each other as shown in the figure,
If the radius of the larger Orange Circle is 9 units and that of the smaller Green circle is 4 units.
What is the radius (correct to two decimal places) of the white circle which lies in between both the circles and also shares the same tangent ?
The answer is 1.44.
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1 solution
Suppose a is the radius of the Orange Circle and b is the radius of the Green circle, Let us assume that c is the radius of the white circle in between...
It can be shown using Pythagoras theorem that
sqrt(ab) = sqrt(bc) + sqrt(ac)
Dividing by sqrt(abc) throughout,
1/sqrt(c) = 1/sqrt(a) + 1/sqrt(b)
Substituting the value of a and b from the problem, we arrive at c = 1.44 units.