# Python: Test if circumference of two circles intersect or overlap

## Python Basic - 1: Exercise-45 with Solution

There are two circles C1 with radius r1, central coordinate (x1, y1) and C2 with radius r2 and central coordinate (x2, y2)

Write a Python program to test the followings -- "C2 is in C1" if C2 is in C1
- "C1 is in C2" if C1 is in C2
- "Circumference of C1 and C2 intersect" if circumference of C1 and C2 intersect
- "C1 and C2 do not overlap" if C1 and C2 do not overlap and
- "Circumference of C1 and C2 will touch" if C1 and C2 touch

**Input:**

Input numbers (real numbers) are separated by a space.

**Pictorial Presentation:**

**Sample Solution**:

**Python Code:**

```
import math
print("Input x1, y1, r1, x2, y2, r2:")
x1,y1,r1,x2,y2,r2 = [float(i) for i in input().split()]
d = math.sqrt((x1-x2)**2 + (y1-y2)**2)
if d <= r1-r2:
print("C2 is in C1")
elif d <= r2-r1:
print("C1 is in C2")
elif d < r1+r2:
print("Circumference of C1 and C2 intersect")
elif d == r1+r2:
print("Circumference of C1 and C2 will touch")
else:
print("C1 and C2 do not overlap")
```

Sample Output:

Input x1, y1, r1, x2, y2, r2: 5 4 2 3 9 2 C1 and C2 do not overlap

Input x1, y1, r1, x2, y2, r2: 5 4 3 5 10 3 Circumference of C1 and C2 will touch

Input x1, y1, r1, x2, y2, r2: 6 4 3 10 4 2 Circumference of C1 and C2 intersect

Input x1, y1, r1, x2, y2, r2: 5 4 3 5 4 2 C2 is in C1

Input x1, y1, r1, x2, y2, r2: 5 4 2 5 4 3 C1 is in C2

**Flowchart:**

**Python Code Editor:**

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