The circumcircleof a triangle is the circle that passes v all 3 vertices the the triangle. The construction an initial establishes the circumcenter and also then color etc the circle.circumcenterof a triangle is the allude where the perpendicular bisectorsof the political parties intersect. This page shows just how to construct (draw) the circumcircle of a triangle through compass and also straightedge or ruler. This building assumes you are currently familiar with building the Perpendicular Bisector that a line Segment.

You are watching: To circumscribe a circle about a triangle you use the

## Printable step-by-step instructions

The above animation is available as a printable step-by-step indict sheet, which deserve to be offered for making handoutsor when a computer system is not available.

## Proof

The image below is the final drawing over with the red brand added.

Note: This proof is virtually identical come the proof inConstructing the circumcenter the a triangle.

See more: Sorting The Field Or Fields On Which The Records Are Sorted, Access Chapter 2 Flashcards

ArgumentReason1JK is the perpendicular bisectorof AB.By construction. For proof seeConstructing the perpendicular bisector that a line segment2Circles exist whose center lies top top the line JK and also of which ab is a chord. (* see keep in mind below)The perpendicular bisector the a chord constantly passes v the circle"s center.3LM is the perpendicular bisector that BC.By construction. Because that proof seeConstructing the perpendicular bisector the a heat segment4Circles exist whose facility lies top top the heat LM and of i m sorry BC is a chord. (* see note below)The perpendicular bisector that a chord constantly passes v the circle"s center.5The point O is the circumcenter the the triangle ABC, the center of the just circle the passes v A,B,C.O is the only allude that lies ~ above both JK and also LM, and so satisfies both 2 and 4 above.5The one O is the circumcircle the the triangle ABC.The one passes with all 3 vertices A, B, C

-Q.E.D

* note Depending where the center point lies on the bisector, over there is one infinite variety of circles the can accomplish this. Two of them are presented below.Steps 2 and 4 work-related together to reduce the possible number to just one.

## Other build pages on this site

### Circles, Arcs and also Ellipses

Tangents to 2 circles (external) Tangents to two circles (internal)

### Non-Euclidean constructions

uncover the center of a circle with any kind of right-angled object