# Triangle: Circumcenter

How to use the property of the circumcenter of a triangle: definition, property, 1 example, and its solution.

## Definition

The circumcenter of a triangle

is the center of the circle

that circumscribes the inner triangle.

## Property

Three perpendicular bisectors of the sides

meet at the circumcenter.

## Example

Solution

Solution (Detail)

It says

point O is the circumcenter.

So, to remind yourself that

point O is the circumcenter,

lightly draw the circumscribed circle.

OM is perpendicular to BC.

Then OM is the perpendicular bisector of BC.

So BM = MC.

See △OBM.

It's a right triangle.

The sides are (3, BM, 5).

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

Pythagorean Triple

So BM = 4.

BM = MC

BM = 4

So MC = 4.

BM = 4

MC = 4

So BC = 4 + 4.

4 + 4 = 8

So BC = 8.