Priyansh Bajaj AskiitiansExpert-IITD
Last Activity: 14 Years ago
Dear Vedanshu,
Solution:- Join origin (say, 'O') to the point (say, 'P') where both the circles are touching. This distance (i.e., OP) will be 'R' (since, it is the radius of bigger circle).
Now, let 'A' and 'B' be the point at which smaller circle is touching coordinate axes x and y respectively. And, center point of smaller circle be 'C'.
Then, OA = r, and OB = r. And, OACB is forming a square of side 'r'.
So, OC = √((OA)2 + (OB)2) = √2 r
Also, OP = OC + CP = √2 r + r = (√2 +1) r = R
or, r = R / (√2 +1) [ANS]
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Priyansh Bajaj