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Analytic Geometry2D

The Circle - Theory & Concepts - Analytic Geometry Three Point Circle

Equations of circles, finding center and radius, tangent lines, and degenerate cases.

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Circle Passing Through Three Points

Point Coordinates

Point A
(-4.0, 3.0)
Point B
(5.0, 4.0)
Point C
(1.0, -4.0)
Matrix System
(−4315411−41)(DEF)=(−25−41−17)\begin{pmatrix} -4 & 3 & 1 \\ 5 & 4 & 1 \\ 1 & -4 & 1 \end{pmatrix} \begin{pmatrix} D \\ E \\ F \end{pmatrix} = \begin{pmatrix} -25 \\ -41 \\ -17 \end{pmatrix}
Cramer's Rule Determinants
det(M) = -68.00
det(D) = 104.00
det(E) = 152.00
det(F) = 1660.00
D = det(D)/det = -1.53, E = det(E)/det = -2.24, F = det(F)/det = -24.41
General Equation
x2+y2−1.53x−2.24y−24.41=0x^2 + y^2 - 1.53x - 2.24y - 24.41 = 0
Standard Equation
(x−0.76)2+(y−1.12)2=26.25(x - 0.76)^2 + (y - 1.12)^2 = 26.25
C(0.8, 1.1)Point A (-4, 3)A(-4, 3)Point B (5, 4)B(5, 4)Point C (1, -4)C(1, -4)

Drag points A, B, and C to dynamically recalculate the circumscribed circle

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