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.
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
Distance between centres C1 and C2 is calculated as
C1C2 = sqrt((x1 – x2)2 + (y1 – y2)2).
There are three conditions that arise.
- If C1C2 <= R1 – R2: Circle B is inside A.
- If C1C2 <= R2 – R1: Circle A is inside B.
- If C1C2 < R1 + R2: Circle intersects each other.
- If C1C2 == R1 + R2: Circle A and B are in touch with each other.
- Otherwise, Circle A and 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)
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