Given the vertices of a triangle and length of its sides. A circle is inscribed in a triangle. The task is to find the incenter of a triangle.
Input: A(2, 2), B(1, 1), C(3, 1) and AB = 2, BC = 1, AC = 1 Output: (2, 1.5) Input: A(3, 3), B(1, 2), C(2, 2) and AB = 3, BC = 2, AC = 2 Output: (2.5, 2.83)
- The centre of the circle that touches the sides of a triangle is called its incenter.
- Suppose the vertices of the triangle are A(x1, y1), B(x2, y2) and C(x3, y3).
- Let the side AB = a, BC = b, AC = c then the coordinates of the in-center is given by the formula:
Below is the implementation of the above approach:
# Python3 program to find the
# incenter of a triangle
# Driver code
# coordinate of the vertices
x1 = 2; x2 = 1; x3 = 3;
y1 = 2; y2 = 1; y3 = 1;
a = 2; b = 1; c = 1;
# Formula to calculate in-center
x = (a * x1 + b * x2 + c * x3) / (a + b + c);
y = (a * y1 + b * y2 + c * y3) / (a + b + c);
print(“Incenter = (“, x, “,”, y, “)”);
# This code is contributed
# by Akanksha Rai
Incenter= (2.0, 1.5)
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