Circumscribed Circle Calculator

Calculate the radius, center, and other properties of a circle that passes through all three vertices of a triangle.

Input Method

Vertex A (x, y)

Vertex B (x, y)

Vertex C (x, y)

R = abc / (4 × Area)

where a, b, c are the sides of the triangle

For vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃):

x = (x₁² + y₁²)(y₂ - y₃) + (x₂² + y₂²)(y₃ - y₁) + (x₃² + y₃²)(y₁ - y₂) / (2(x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)))

y = (x₁² + y₁²)(x₃ - x₂) + (x₂² + y₂²)(x₁ - x₃) + (x₃² + y₃²)(x₂ - x₁) / (2(y₁(x₃ - x₂) + y₂(x₁ - x₃) + y₃(x₂ - x₁)))

Note: The circumscribed circle (circumcircle) passes through all three vertices of the triangle. Its center is called the circumcenter.

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