Let us see another illustration of generalisation of a result
Problem Description : Two circles of radii R and r touch each other externally. Find the radius r1 of circle touching both these externally and their direct common tangent. Also find the radius r2 of circle which touches the second and third circles and their direct common tangent.
Solution :
From the above figure, we get the radius r1 as
Similarly, we get r2 as
Now by substituting
we get
Generalisation : Proceeding like this the radius rn of nth such circle is
Problem Description : Two circles of radii R and r touch each other externally. Find the radius r1 of circle touching both these externally and their direct common tangent. Also find the radius r2 of circle which touches the second and third circles and their direct common tangent.
Solution :
From the above figure, we get the radius r1 as
Similarly, we get r2 as
Now by substituting
we get
Generalisation : Proceeding like this the radius rn of nth such circle is
thanks to prof.JN Kapoor through his books i cold get to the glimpses of the idea of what generalisation of a result means in maths
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