Circle Meets Rectangle

Medium

A plane holds a circle centered at (cx, cy) with radius r, and an axis-aligned rectangle whose bottom-left corner is (left, bottom) and top-right corner is (right, top). Both shapes are filled and include their boundary. Return True if they share at least one point, and False otherwise.

Example 1

r=2, cx=0, cy=0, left=2, bottom=-1, right=5, top=4 → True

The circle touches the rectangle's left side at (2, 0), so they share a point.

Example 2

r=2, cx=0, cy=0, left=2, bottom=2, right=6, top=5 → False

The closest point of the rectangle is the corner (2, 2), which is 2√2 ≈ 2.83 > 2 away.

Example 3

r=1, cx=3, cy=3, left=0, bottom=0, right=10, top=10 → True

The whole disk lies inside the rectangle.

Constraints

1 ≤ r ≤ 2000
-10⁴ ≤ cx, cy ≤ 10⁴
-10⁴ ≤ left < right ≤ 10⁴
-10⁴ ≤ bottom < top ≤ 10⁴

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Topics

Geometry Math

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Input

r=2, cx=0, cy=0, left=2, bottom=-1, right=5, top=4

Expected

True

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