# Circumcenter of a Triangle

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

## Definition

The circumcenter of a triangle

is the center of the circle

that circumscribes the triangle.

## Properties

Property 1:

The distances

between the circumcenter and each vertex

are the same.

Property 2:

Three perpendicular bisectors of the triangle's sides

meet at the circumcenter.

## Example

It says point *O* is the circumcenter.

So *OM* is the perpendicular bisector of *BC*.

So *BM* = *MC*.

See △*OBM*.

It's a right triangle.

And starting from the shortest side,

the sides are (3, *BM*, 5).

So △*OBM* is a (3, 4, 5) right triangle.

Pythagorean triples

So *BM* = 4.

*BM* = 4

And *BM* = *MC*.

So *MC* is also 4.

So *BC* = 4 + 4

= 8.