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Triangle Centers

What do the orthocenter, centroid, and circumcenter share in common? They lie on the Euler line!

Triangle Centers Warmup


True or False?

The six small triangles within the larger triangle are equal in area.

Every triangle has a circumcenter, the center of the circle that can be circumscribed about the triangle. Is the following statement true or false?

The circumcenter of a triangle can lie inside of, outside of, or on a triangle.

A developer wants to construct a shopping center that is equidistant from three towns. If the three towns form the vertices of a triangle, his shopping center should be at the intersection of the __ of the triangle.

The strength of John's imaginary triangular shaped energy vortex is strongest at the point that is equidistant from the sides of the triangle. John could find this point by finding the intersection of the:

Willa sits at her desk, attempting to balance a triangular plaque on her pencil. To find the balance point, she should find the intersection of the:


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