The circumcenter is the point of intersection for the three perpendicular bisectors of a triangle.
First, you need to calculate the perpendicular bisectors for each side:
1. Choose a side of the triangle to start with. Calculate the perpendicular bisectors by starting at the midpoint of the side and creating a line that is of the opposite slope of the side. Extend the line until it has completely crossed through the triangle. Write the equation for this line in point-slope form.
2. Repeat with one of the remaining sides.
3. Calculate the point of intersection of the two lines you just created. To do this, take the two equations of the lines and use substitution.
For example, if you have y = 2x + 1 and y = x - 1, write "2x + 1 = x - 1". You are basically eliminatig the ys.
3. Solve for x, then substitute the x value into one of your point-slope equations to solve for y. Put the x and y in an ordered pair, and you have the circumcenter.
