Given coordinate of the center and radius > 1 of a circle and the equation of a line. The task is to check if the given line collide with the circle or not. There are three possibilities :
- Line intersect the circle.
- Line touches the circle.
- Line is outside the circle.
Note: General equation of a line is a*x + b*y + c = 0, so only constant a, b, c are given in the input.
Input : radius = 5, center = (0, 0), a = 1, b = -1, c = 0. Output : Intersect Input : radius = 5, center = (0, 0), a = 5, b = 0, c = 0. Output : Touch Input : radius = 5, center = (0, 0), a = 1, b = 1, c = -16. Output : Outside
The idea is to compare the perpendicular distance between center of circle and line with the radius of the circle.
1. Find the perpendicular (say p) between center of circle and given line.
2. Compare this distance p with radius r.
……a) If p > r, then line lie outside the circle.
……b) If p = r, then line touches the circle.
……c) If p < r, then line intersect the circle.
How to find the perpendicular distance ?
Distance of a line from a point can be computed using below formula:
Refer Wiki for details of above formula.
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Improved By : Sam007