The circumcentre of a triangle is equidistant from each of the vertices
of a triangle. That is, each side of the triangle becomes a chord of the circle,
and the triangle lies totally within the circle circumscribing it.
The incentre of a triangle is the point which is equidistant from each of the sides. That is, each side of the triangle becomes a tangent to the circle,
and the circle lies totally within the triangle.
Two other centres of a triangle would be of interest to you:
the centroid, which is the intersection of the medians of a triangle, and
the orthocentre, which is the intersection of the altitudes of a triangle.
Of further interest is the fact that the orthocentre, the centroid and the circumcentre all lie on the same straight line, called Euler's Line.
what are the properties of the circumcenter of a triangle?
what are the properties of an incenter triangle?
1 answer
1 answer