# Python: Compute the radius and the central coordinate (x, y) of a circle which is constructed by three given points on the plane surface

## Python Basic - 1: Exercise-39 with Solution

Write a program to compute the radius and the central coordinate (x, y) of a circle which is constructed from three given points on the plane surface.

**Input:**

x1, y1, x2, y2, x3, y3 separated by a single space.

**Sample Solution**:

**Python Code:**

```
# Prompt the user to input three coordinates of the circle
print("Input three coordinates of the circle:")
x1, y1, x2, y2, x3, y3 = map(float, input().split())
# Calculate distances between points
c = (x1 - x2)**2 + (y1 - y2)**2
a = (x2 - x3)**2 + (y2 - y3)**2
b = (x3 - x1)**2 + (y3 - y1)**2
# Calculate the cross-product
s = 2 * (a * b + b * c + c * a) - (a**2 + b**2 + c**2)
# Calculate the central coordinate of the circle
px = (a * (b + c - a) * x1 + b * (c + a - b) * x2 + c * (a + b - c) * x3) / s
py = (a * (b + c - a) * y1 + b * (c + a - b) * y2 + c * (a + b - c) * y3) / s
# Calculate the radius of the circle
ar = a**0.5
br = b**0.5
cr = c**0.5
r = ar * br * cr / ((ar + br + cr) * (-ar + br + cr) * (ar - br + cr) * (ar + br - cr))**0.5
# Print the radius and central coordinate of the circle
print("Radius of the said circle:")
print("{:>.3f}".format(r))
print("Central coordinate (x, y) of the circle:")
print("{:>.3f}".format(px), "{:>.3f}".format(py))
```

Sample Output:

Input three coordinate of the circle: 9 3 6 8 3 6 Radius of the said circle: 3.358 Central coordinate (x, y) of the circle: 6.071 4.643

**Explanation:**

The above Python code takes as input three pairs of coordinates representing the points on a circle. It then calculates the radius and central coordinate of the circle based on these input coordinates using geometric formulas. Here's a step-by-step explanation:

- Input Coordinates:
- The user is prompted to input three pairs of coordinates (x, y) representing points on a circle.
- Calculate Distances:
- The code calculates the squared distances between pairs of points using the distance formula.
- Calculate Cross-Product and Central Coordinate:
- It computes a cross-product and uses it to calculate the central coordinates (px, py) of the circle.
- Calculate Radius:
- The code computes the radius of the circle using the squared distances between points.
- Print Results:
- The radius and central coordinates of the circle are printed with three decimal places.

**Flowchart:**

**Python Code Editor:**

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