Welcome to the Circumcenter of a triangle, Geometry Index.

Circumcenter/Circumcircle of a triangle - Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Triangle Centers.

Perpendicular Bisector.

GeoGebra, Dynamic Geometry: Circumcenter and Circumcircle of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Distances between Triangle Centers Index.

GeoGebra, Dynamic Geometry: Euler Line of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Nine-Point Center, Nine-Point Circle, Euler Line (English version).
Circumcenter, Centroid, Orthocenter
Interactive illustration.

van Lamoen Circle - Index.

Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence.

Geometry Problem 847
van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points.

Geometry Problem 846
Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral, Similarity.

Geometry Problem 845
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 844
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 843
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Parallel, Congruence, Similarity.

Geometry Problem 842
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 841
Triangle, Medians, Centroid, Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 837
Triangle, Orthocenter, Circumcenter, Circle, Concyclic Points.

Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity.

Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter.

Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle.

Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence.

Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance.

Geometry Problem 774
Triangle, Two Altitudes, Circumcircle, Tangent at a Vertex, Parallel.

Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement.

Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence.

Geometry Problem 742.
Scalene Triangle, Orthocenter, Centroid, Circumcenter, Circumradius, Midpoint, Distance, Square, Metric Relations.

Geometry Problem 741.
Scalene Triangle, Incenter, Circumcircle, Midpoint, Arc, Congruence.

Geometry Problem 733.
Triangle, Orthocenter, Altitude, Reflection in a line, Circumcircle, Concurrency.

Geometry Problem 729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Midpoint.

Geometry Problem 728.
Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency.

Geometry Problem 706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral.

Geometry Problem 675.
Circumcircles, Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points.

Geometry Problem 670.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Circumcircle Congruence.

Triangle Circumcenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map.

Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Circumcircle, Angles, Triangle centers.

Geometry Problem 662.
Triangle, Incenter, Circumcenter, Circumcircle, Orthocenter, Circle, Angle, Measurement.

Geometry Problem 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Geometry Problem 593.
Triangle, Circumcircle, Collinear Points.

Problem 585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.

Problem 584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms.

Problem 583.
Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelogram, Octagon, Areas.

Problem 548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points, Similarity.

Problem 547.
Triangle, Transversal, Four Circumcircles, Circumcircles, Concurrency.

Problem 538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint.

Problem 535.
Sawayama - Thebault's theorem: Triangle, Incircle, Circle, Circumcircle, Center, Tangent, Collinear.

Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area.

Problem 526.
Equilateral Triangle, Circumcircle, Chord, Measurement.

Problem 476.
Triangle, Circumcenter, Circumcircle, Angles.

Proposed Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius, Circumcenter, Circumcircle.

Proposed Problem 426.
Triangle, Circumradius, Circumcenter, Circumcircle, concurrent Cevians.

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.
Puzzle based on poblem 401.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Puzzle: Euler Line and Nine Point Center

Schiffler Point: Four Euler Lines with interactive animation and manipulation.
Circumcenter, Circumcircle, Centroid, Orthocenter, and Incenter.

Interactive Simson Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Circumcenter O.

Angle between two Simson Lines. Proof with animation.
 

Simson Line. A proof of Simson line with animation.

Triangle, Three Medians, Six Concyclic Circumcenters. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Proposed Problem 209. Circumcenter of the contact triangle.
Triangle, Incircles, Inradius.

Journey to the Center of a Triangle (1976). Incenter, Circumcenter, Centroid, Orthocenter.

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.

Feuerbach Point Facts.
Distances between Feuerbach point and the incenter, nine-point center, centroid, Spieker point, and Circumcenter

Spieker Center

Interactive Gergonne Line and Nobbs Points. Circumcenter of the contact triangle.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.

Steiner Point
Circumcenter, Lemoine Point. 

Symmedian (Lemoine) Point
Triangle Center

Sangaku Problem (An Old Japanese Theorem). Inradii, Carnot's theorem.

Carnot Theorem. Circumcenter, circumradius, inradius

Steiner Theorem. Circumcenter, circumradius, inradius, exradii

Geometry Online Glossary .
Geometry Glossary based on the new New York State mathematics standards initiative.

Right Triangle: Circumcenter. Centers, Inradius, Circumradius, Incenter, Circumcenter, Orthocenter, Centroid, Poncelet's theorem, Sagitta.

Proposed Problem 160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.  

Proposed Problem 159. Distances from the Circumcenter to the Incenter and the Excenters.  

Proposed Problem 158. Circumcenter
 Relation between the Circumradius, Inradius and Exradii of a triangle.  

Proposed Problem 157. Distance from the Circumcenter to the Excenter.  

Proposed Problem 156. Circumcenter
Triangle, Circumradius, Exradius, Chord, Secant line.  

Proposed Problem 155. Euler's Theorem: Distance from the Incenter to the Circumcenter.  

Proposed Problem 154. Circumcenter.
Triangle, Inradius, Circumradius, Chord.

Proposed Problem 145. Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters.

Proposed Problem 143. Circumcenter.
Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.

Proposed Problem 139. Circumcenter.
Triangle Area, Orthic Triangle, Semiperimeter, Circumradius.  

Proposed Problem 138. Circumcenter.
Nagel's Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.  

Proposed Problem 94. Circumcenters.
Similar Triangles, Circumcircles, Circumradii.

Proposed Problem 93. Circumcenters.
Similar Triangles, Circumcircles, Parallelogram.

Proposed Problem 92. Circumcenters.
Similar Triangles, Circumcircles, Circumradii, Parallel.

Proposed Problem 86. Circumcenter of the intouch triangle.
Intouch and Extouch Triangles, Areas.

Intouch and Extouch Triangles. Puzzle cut: 20 Piece Classic
Based on Proposed Problem 86.

Proposed Problem 83. Circumcenter.
Area of the Excircle Contact Triangle, exradius, circumradius.

Proposed Problem 82. Circumcenter.
Area of the Contact Triangle, inradius, circumradius.

Proposed Problem 81. Circumcenter.
Area of a triangle, side, inradius, circumradius.

Proposed Problem 67: Circumcenter
Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
 

Miquel's Pentagram with Dynamic Geometry. Circumcenters.
You can alter the pentagram dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

Miquel's Pentagram Theorem Interactive proof with animation and key theorems.
 

Adams' Circle Theorem. Circumcenter of the contact triangle
 

Lemoine Theorem. Circumcenter.

Sawayama -Thebault's theorem. Circumcenter.

Circulo de los Nueve Puntos: Spanish version.

Nine-Point Center, Nine-Point Circle, Euler Line (English version) .
Interactive illustration.

The Bevan Point The circumcenter of the excentral triangle. Illustration with animation.

The Bevan Point: Puzzle The circumcenter of the excentral triangle.

Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Proposed Problem 247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.

Proposed Problem 246.
Napoleon's Theorem I. External Equilateral triangles.