The circumcircleof a triangle is the circle the passes v all 3 vertices the the triangle. The construction an initial establishes the circumcenter and then paint, etc the circle.circumcenterof a triangle is the point where the perpendicular bisectorsof the sides intersect. This web page shows just how to build (draw) the circumcircle that a triangle v compass and also straightedge or ruler. This building and construction assumes you are currently familiar with building the Perpendicular Bisector of a heat Segment.

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Printable step-by-step instructions

The over animation is accessible as a printable step-by-step accuse sheet, which have the right to be provided for making handoutsor as soon as a computer is not available.


Proof

The image listed below is the final drawing above with the red labels added.

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

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

-Q.E.D


* keep in mind Depending whereby the center suggest lies on the bisector, there is an infinite number of circles that can accomplish this. 2 of lock are shown below.Steps 2 and also 4 job-related together to alleviate the possible number to simply one.

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Other constructions 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

discover the facility of a circle with any right-angled object