# A Large Circle Has A Radius Of 10cm. Find The Radius Of The Largest Circle Which Will Fit In Da Middle.?

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## A large circle has a radius of 10cm. Find the radius of the largest circle which will fit in da middle.?

The radius of the big circle is R = 10cm.

In your case the 4 inner cirles will have a radius we can call “r”. The centers of these circles form a square of “2r” per side. The diagonal of this square will measure “2r*sqrt(2)”. By extending this diagonal of “2r ” (r on each side) we get the diameter of the big circle (20cm = 2R).

So 2r*sqrt(2) + 2r = 2R => r = R / (1 + sqrt(2))

If we call “n” the radius of the smaller inner circle, the diagonal is also “2r + 2n”.

So 2r*sqrt(2) = 2r + 2n => n = r(sqrt(2) – 1)

=> n = R / (1 + sqrt(2))(sqrt(2) – 1)

=> n = R (sqrt(2) – 1) (sqrt(2) – 1) = 1.7 cm

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