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Find the radius of the circle of least area that is tangent to the curve y = 4 - x² and to the pair of lines y = |x|.

1. 4(sqrt(2) - 1)
2. 4(sqrt(2) + 1)
3. 2(sqrt(2) + 1)
4. 2(sqrt(2) - 1)

Correct answer: 4(sqrt(2) - 1)

Solution

Placing the centre at (0,k) on the axis of symmetry, the tangency to y = |x| gives r = k/sqrt(2), and tangency to the parabola (touching the lower side) yields r = 4(sqrt(2) - 1) for the minimum-area circle.

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