1. What is the Circumcenter?

The circumcenter of a triangle is the point where the perpendicular bisectors of the triangle's sides intersect. It is the center of the circumcircle - the circle that passes through all three vertices of the triangle.

2. How Does the Calculator Work?

The calculator finds the intersection point of two perpendicular bisectors:

3. Importance of Circumcenter

Details: The circumcenter is important in geometry for constructing circumcircles, solving triangle problems, and has applications in computer graphics, navigation, and engineering design.

4. Using the Calculator

Tips: Enter the (x,y) coordinates of three non-collinear points that form a triangle. The calculator will find the circumcenter coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can the circumcenter be outside the triangle?
A: Yes, in obtuse triangles the circumcenter lies outside the triangle. In acute triangles it's inside, and in right triangles it's on the hypotenuse.

Q2: What if the points are collinear?
A: Collinear points don't form a triangle, so there is no circumcenter. The calculator will return "undefined".

Q3: How accurate is the calculation?
A: The calculator provides results rounded to 4 decimal places, which is sufficient for most practical applications.

Q4: Can I use this for 3D coordinates?
A: No, this calculator only works for 2D coordinates. The circumcenter concept extends to 3D but requires different calculations.

Q5: What's the relationship between circumradius and circumcenter?
A: The circumradius is the distance from the circumcenter to any vertex. You can calculate it using the distance formula.