Posted by **Zach** on Thursday, November 15, 2012 at 8:25pm.

Help I need help to find the coordinates of the circumcenter of each triangle. Isosceles triangle CDE with vertices C(0, 6), D(0, –6), and E(12, 0)

- Geometry -
**Steve**, Thursday, November 15, 2012 at 11:56pm
the circumcenter is the intersection of the perpendicular bisectors of the sides.

The midpoint of CD = (0,0)

The slope of CD is -12/0 is undefined, so CD is vertical

The perpendicular bisector is horizontal.

You want the line through (0,0) with slope 0 is the line y=0.

The midpoint of DE = (6,-6)

The slope of DE is 6/12 = 1/2

You slope of the bisector is -2

The line through (6,-6) with slope -2 is

y+6 = -2(x-6), or y = -2x + 6

the two bisectors intersect at (0,3), which is the circumcenter.

as usual, check my math.

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