Circumcenter

A circumcenter is the point of concurrency of the three perpendicular bisectors. -Construct triangle XYZ and label the vertices with text toolToolbar Image. -Construct the perpendicular bisector Toolbar Imageof each side. -Use the intersect Toolbar Imagein the point menu to mark the circumcenter and name it A with text tool Toolbar Image.
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Construct the circumcenter below.

Drag the vertices of XYZ around. What kind of triangle is XYZ if the circumcenter A falls on the exterior of the triangle?

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What kind of triangle is XYZ if the circumcenter A falls on the triangle?

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What kind of triangle is XYZ if the circumcenter A is in the interior of the triangle?

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A circumscribed circle (circle that goes through each vertex) can be added in this construction above. Draw a segment from the circumcenter A to vertex X. This creates the radius of the circle (segment AX). Construct a circle on your construction above using your compass toolToolbar Image. Move the triangle around and verify the circle always goes through all vertices X, Y and Z.
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Drag around the vertices of XYZ. Does the circle always go through the three vertices and remain outside the triangle?

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Since a circumscribed circle goes through each vertex, the circumcenter is equidistant from each:

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