Check if a line touches or intersects a circle in C++

Suppose we have a circle and another straight line. Our task is to find if the line touches the circle or intersects it, otherwise, it passes through outside. So there are three different cases like below −

Here we will solve it by following steps. These are like below −

• Find perpendicular P between the center and given a line
• Compare P with radius r −
  • if P > r, then outside
  • if P = r, then touches
  • otherwise inside

To get the perpendicular distance, we have to use this formula (a center point is (h, k))

$$\frac{ah+bk+c}{\sqrt{a^2+b^2}}$$

Example

 Live Demo

#include <iostream>
#include <cmath>
using namespace std;
void isTouchOrIntersect(int a, int b, int c, int h, int k, int radius) {
   int dist = (abs(a * h + b * k + c)) / sqrt(a * a + b * b);
   if (radius == dist)
      cout << "Touching the circle" << endl;
   else if (radius > dist)
      cout << "Intersecting the circle" << endl;
   else
      cout << "Outside the circle" << endl;
}
int main() {
   int radius = 5;
   int h = 0, k = 0;
   int a = 3, b = 4, c = 25;
   isTouchOrIntersect(a, b, c, h, k, radius);
}

Output

Touching the circle

Arnab Chakraborty

Updated on 22-Oct-2019 08:33:53

• Related Questions & Answers
• Check if a circle lies inside another circle or not in C++
• Check If It Is a Straight Line in C++
• Check if a line passes through the origin in C++
• How to create a line chart using ggplot2 that touches the edge in R?
• C++ Program to Check if a Point d lies inside or outside a circle defined by Points a, b, c in a Plane
• C++ Program to Check if a Given Set of Three Points Lie on a Single Line or Not
• Check if two line segments intersect
• Check if a word exists in a grid or not in Python
• Check if a given graph is tree or not
• How to check if a field in MongoDB is [] or {}?
• Check if a number is jumbled or not in C++
• Check if input is a number or letter in JavaScript?
• Check if a Tree is Isomorphic or not in C++
• Check if a string is Isogram or not in Python
• Check if a Java ArrayList contains a given item or not