You are watching: Which point in a triangle is equidistant from the vertices of the triangle?

The circumcenter of a triangle is the suggest wright here the 3 perpendicular bisectors of a triangle accomplish. It is likewise the center of the circumcircle (the circle that goes via the vertices of the triangle). Sometimes the circumcenter is exterior of the triangle, itself.

Think around what that means: What do you know around circles? What is the facility of a circle? The facility of a circle is equifar-off to all points on the circle. This implies that the circumcenter is equiremote to every one of the vertices of the triangle given that the circumcircle touches all 3 vertices.

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