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


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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.

Try it yourself

Other build pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and also Ellipses

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

Polygons

Non-Euclidean constructions

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