Thursday, March 26, 2009

Circle Circumscribing a Triangle

Triangle ABC Given a triangle ABC in R2, there is exactly one circle that goes through the points. How do you find the circle?

I'll assume you know how to construct the perpendicular bisector of a line segment.

Any circle that touches both A and B must have its center on the perpendicular bisector of AB.

Similarly, any circle that touches both A and C must have its center on the perpendicular bisector of AC.

The circle we are looking for has its center at the intersection of those two bisectors, and the radius is determined from that center point to any of the three original points.

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About Me

I'm research faculty at MIT, and Chief Architect at Tokutek.