Circumcenter, Circumcircle, Circumradius of a triangle, Geometry, Theorems and Problems

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.

Lester Circle Theorem.
Circumcenter.

van Lamoen Circle - Index.

Geometry Problem 1605: Triangle, Angle Bisector, and Circumcircle

Geometry Problem 1583: Prove Lines CK and BL are Parallel.

Geometry Problem 1582: Prove That Angles AFD and AEF Are Equal in This Secant Problem.

Geometry Problem 1581: Prove the Angle Bisection in a Cyclic Quadrilateral.

Geometry Problem 1561: Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle Secrets.

Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors

Geometry Problem 1551: Unraveling Angle Relations in Cyclic Quadrilaterals: Solving for Angle GEJ: A High School Level Investigation

Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit.

Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1478.
Cyclocevian, Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration.

Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration.

Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration.

Geometry Problem 1457.
Altitudes, Circles, Similarity, Product of the Inradii Lengths, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third Area, Art, Poster, Typography, iPad Apps.

Geometry Problem 1438.
Triangle, Incenter, Centroid, Circumcenter, Parallel, 90 Degree, Art, Poster, Typography, iPad Apps.

Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping.

Geometry Problem 1423.
Triangle, Area, Three Equal Angles, Circumradius, Measurement.

Geometry Problem 1419.
Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint.

Geometry Problem 1418.
Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle.

Geometry Problem 1417.
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector, Tangent Lines, Tangent Circles.

Geometry Problem 1399.
Triangle, Circumcircle, Perpendiculars, Angles, Congruence, Cyclic Quadrilateral.

Geometry Problem 1391.
Two Triangles, Ratio of Areas, Circumcircle.

Geometry Problem 1385.
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points.

Geometry Problem 1384.
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree.

Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints.

Geometry Problem 1347.
Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle.

Problem 1341.
Geometry Problem 1341: Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.

Problem 1337.
Parallelogram, Diagonals, Circle, Circumcircle, Tangent Line, Triangle, Congruence.

Geometry Problem 1322.
Triangle, Angle Bisector, Circumcircle, Chord, Secant, Sum of two Angles.

Geometry Problem 1319.
Hexagons, Equilateral Triangles, Center, Midpoints.

Geometry Problem 1312.
Triangle, 60 Degrees, Circle, Circumcenter, Orthocenter, Altitude, Distance, Perpendicular, Measurement.

Geometry Problem 1311.
Inscribed Triangle, Circle, Circumcircle, Concyclic Points, Measurement.

Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area.

Geometry Problem 1277.
Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement.

Geometry Problem 1276.
Equilateral Triangle, Circumcircle, Internally Tangent Circles, Tangent Line, Measurement.

Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement.

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