Circumcenter of a Triangle
How to solve the circumcenter of a triangle problems: definition, properties, example, and its solution.
The circumcenter of a triangle
is the center of the circle
that circumscribes the triangle.
So the distances between the circumcenter
and each vertex of a triangle
are the same.
Three perpendicular bisectors of the triangle's sides
meet at the circumcenter.
Point O is the circumcenter.
And OM (blue) is perpendicular to BC.
So OM is the perpendicular bisector of BC.
This means BM = MC.
△OBM is a (3, 4, 5) right triangle.
So BM = 4.
Then BM = MC = 4.
BM = MC = 4.
So BC = 4 + 4 = 8.