# Circumcenter of a Triangle

How to solve the circumcenter of a triangle problems: definition, properties, example, and its solution.

## Definition

The circumcenter of a triangle

is the center of the circle

that circumscribes the triangle.

## Properties

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.

## Example

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.

Pythagorean triples

Then *BM* = *MC* = 4.

*BM* = *MC* = 4.

So *BC* = 4 + 4 = 8.