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Circle K is the largest circle that can be inscribed in the first quadrant (touching both coordinate axes) while also touching the circle x² + y² = 36 internally. Find the radius of circle K.

1. (6 - sqrt(2))/2
2. 3*sqrt(2)/2
3. 3
4. 6(sqrt(2) - 1)

Correct answer: 6(sqrt(2) - 1)

Solution

Centre (r,r) is at distance r*sqrt(2) from the origin; internal tangency gives r*sqrt(2) = 6 - r, so r = 6/(sqrt(2)+1) = 6(sqrt(2)-1).

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