Plane Geometry: Circumcircle of a Triangle, Circumcenter, Circumradius

Circumcircle of a triangle - Table of Content

Triangle Centers.

Distances between Triangle Centers Index.

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

Poly for iPad.
Polygonal Art, Delaunay Triangulation.

Lemoine Line Theorem, Interactive illustration.
HTML5 Animation for iPad and Nexus

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

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

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

Geometry Problem 829
Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations.

Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint.

Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram.

Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular.

Geometry Problem 780
Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices.

Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.

Geometry Problem 777
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Cosine.

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 757
Equilateral Triangle, Circumcircle, Chords, a Half of Harmonic Mean.

Geometry Problem 755.
Equilateral Triangle, Circumcircle, Chord, Arc, Midpoints, Perpendicular.

Geometry Problem 738.
Intersecting Circles, External Common Tangent, Common Chord, Secant, Circumcircle, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 721.
Triangle, Orthocenter, Circumcircle, Altitude, Collinear points.

Geometry Problem 715.
Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement.

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

Geometry Problem 702.
Triangle, Circumcircle, Parallel, Concyclic Points.

Problem 476.
Triangle, Circumcenter, Circumcircle, Angles.

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

Proposed Problem 426.
Triangle, Circumcircle, Circumradius, Circumcenter, 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.
Circumcircle, Circumcenter, Centroid, Orthocenter, and Incenter.

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

Angle between two Simson Lines. Proof with animation.
Circumcircle 

Simson Line. A proof of Simson line with animation.
Circumcircle.

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

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

Journey to the Center of a Triangle (1976). Incenter, Circumcircle, 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, Circumcircle.

Steiner Point
Circumcircle, Circumcenter, Lemoine Point. 

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

Carnot Theorem. Circumcircle, Circumcenter, circumradius, inradius

Steiner Theorem. Circumcircle, 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. Circumcircle, Distances from the Circumcenter to the Incenter and the Excenters.  

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Miquel's Pentagram with Dynamic Geometry. Circumcircles, 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.
Circumcircles, Circumcenters.

Adams' Circle Theorem. Circumcircle, Circumcenter of the contact triangle
 

Lemoine Theorem. Circumcircle, Tangent, Collinear points.

Sawayama -Thebault's theorem. Circumcircle, Incircle, Collinear points.

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

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