UPSC 2015 CDS I Math Paper

Let the radius of the in circle be r.The lengths of the tangents drawn from an external point to the circle are equal.
∴ BD = BE = r
CD = CF= b-r
AE = AF= a - r
Now AF + CF = c
⇒a−r+b−r=c
⇒2r=a+b−c
⇒r=

a+b−c

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