Check if two given circles touch or intersect each other

There are two circles A and B with their centres C1(x1, y1) and C2(x2, y2) and radius R1 and R2. The task is to check both circles A and B touch each other or not.

Examples :

Input : C1 = (3,  4)
        C2 = (14, 18)
        R1 = 5, R2 = 8
Output : Circles do not touch each other.

Input : C1 = (2,  3)
        C2 = (15, 28)
        R1 = 12, R2 = 10
Output : Circles intersect with each other.

Input : C1 = (-10,  8)
        C2 = (14, -24)
        R1 = 30, R2 = 10

Approach:
Distance between centres C1 and C2 is calculated as

 C1C2 = sqrt((x1 - x2)^{2 +} (y1 - y2)²).

There are three conditions that arise.

1. If C1C2 <= R1 - R2: Circle B is inside A.
2. If C1C2 <= R2 - R1: Circle A is inside B.
3. If C1C2 < R1 + R2: Circle intersects each other.
4. If C1C2 == R1 + R2: Circle A and B are in touch with each other.
5. Otherwise, Circle A and B do not overlap

Below is the implementation of the above approach: 

Circle touch to each other

Time Complexity: O(log(n)) because using inbuilt sqrt function 
Auxiliary Space: O(1)

This article is contributed by Aarti_Rathi and Dharmendra kumar.