The Circumcenter is the magical point equidistant from all three vertices of a triangle. It is the center of the “Circumcircle” that passes perfectly through every corner. The Circumcenter of Triangle Calculator computes this point’s coordinates and the radius of the circle using rigorous coordinate geometry.
Features
Perpendicular Bisectors: Mathematically replicates the intersection of perpendicular bisectors.
Full Output: Provides coordinates (Ux, Uy) and the Circumradius (R).
Visual Graph: Draws the triangle, the circumcenter, AND the circumcircle surrounding it.
Collinear Check: Detects if points form a straight line (no circle possible).
How to Use This Calculator
Input Vertices: Enter the x and y values for points A, B, and C.
Locate Center: Click calculate to solve the system of equations.
Analyze: Look at the derived Radius and Center coordinates.
See it: The canvas draws dashed bisectors (conceptually) or the circle itself.
Formulas
The calculator uses the following mathematical principles:
Determinant (D): $$ D = 2(x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)) $$
Center X: $$ Ux = \frac{1}{D} [ (x_1^2+y_1^2)(y_2-y_3) + … ] $$
Center Y: $$ Uy = \frac{1}{D} [ (x_1^2+y_1^2)(x_3-x_2) + … ] $$
Practical Applications
Location Planning: Finding a location equidistant from three existing sites (e.g., a cell tower serving 3 towns).
Robotics: Path planning to avoid obstacles by moving in circular arcs defined by control points.
Pattern Making: Constructing circles that fit specific boundary points.
Tips for Success
Position: The circumcenter can be inside (Acute), outside (Obtuse), or exactly on the midpoint of the hypotenuse (Right) of the triangle.
Singularity: If the three points lie on a straight line, the circle has infinite radius (no solution).
Precision: Coordinates are calculated to high decimal precision.
Frequently Asked Questions (FAQ)
Why is the center outside my triangle?
For a Right Triangle, correct?
What is the Circumradius?
It is the radius of the circle that touches all three vertices.
Final Words
Connecting the dots has never been more scientific. The Circumcenter of Triangle Calculator solves one of the most useful problems in spatial geometry, helping you find the one point that treats all corners equally.
