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![College Geometry Online, eLearning](../machu_picchu_h1_810.jpg)
Circumcenter, Circumcircle, Circumradius of a triangle, Geometry, Theorems and Problems
Circumcircle's realm,
Encircling geometric forms,
Radiant embrace.
Centered in symmetry's arms,
Geometry's celestial grace.
![Circumcenter Index](circumcenter_index_17.jpg)
|
![Euclid's Elements 23 definitions](../geometry/euclid_elements_definition_170.jpg) |
Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's
Elements Book. Index |
![](../triangle_center_170.jpg) |
Triangle Centers. |
![Perpendicular Bisector Index](../math_geometry_online_courses/perpendicular_bisector_i_1.jpg) |
Perpendicular
Bisector. |
![Dynamic Geometry: Circumcenter and Circumcircle of a Triangle. HTML5 Animation for Tablets (iPad, Nexus..)](../geogebra/geogebra-triangle-circumcenter-circumcircle-html5-animation-ipad-nexus-1.jpg) |
GeoGebra, Dynamic Geometry: Circumcenter and Circumcircle
of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..) |
![Distance between triangle centers](distance_triangle_centers.jpg) |
Distances between Triangle Centers
Index.
|
![Dynamic Geometry: Euler Line of a Triangle. HTML5 Animation for Tablets (iPad, Nexus..)](../geogebra/geogebra-triangle-euler-line-html5-animation-ipad-nexus-1.jpg) |
GeoGebra, Dynamic Geometry:
Euler Line
of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..) |
![](nine_point_center_euler_170.jpg) |
Nine-Point Center, Nine-Point Circle, Euler Line (English
version).
Circumcenter, Centroid, Orthocenter
Interactive illustration.
|
![Lester Circle Theorem](../circle/lester-circle-fermat-circumcenter-nine-point-college-1.jpg) |
Lester Circle Theorem.
Circumcenter. |
![van Lamoen Circle Index](../geometry/triangle-centroid-six-circumcenters-van-lamoen-circle-index-1.jpg) |
van Lamoen Circle - Index. |
![Geometry Problem 1561](../school-college/6/p1561-highschool-college-geometry-triangle-ABC-circumcenter-orthocenter-angle-parallel-problem-1.jpg) |
Geometry Problem 1561:
Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle
Secrets. |
![Geometry Problem 1553](../school-college/6/p1553-triangle-abc-angle-bisectors-calculate-circumradius-1.jpg) |
Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors |
![Geometry Problem 1551](../school-college/6/p1551-angle-relations-cyclic-quadrilateral-abcd-circumcircles-triangles-1.jpg) |
Geometry Problem 1551: Unraveling Angle Relations in Cyclic Quadrilaterals: Solving for Angle GEJ: A High School Level Investigation |
![Geometry Problem 1541](../school-college/6/p1541-inscribed-cyclic-quadrilateral-diameter-circumcircle-harmonic-quaternary-menelaus-ceva-1.jpg) |
Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit. |
![Dynamic Geometry 1479](../school-college/5/p1479-triangle-circumcircle-angle-perpendicular-bisector-parallel-concyclic-geogebra-ipad-1.jpg) |
Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector,
Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1478](../school-college/5/p1478-reuschle-terquem-theorem-3-cevians-circumcircle-concurrent-geogebra-ipad-1.jpg) |
Dynamic Geometry 1478.
Cyclocevian, Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1477](../school-college/5/p1477-miquel-pentagram-theorem-circumcircle-5-concyclic-geogebra-ipad-1.jpg) |
Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1473](../school-college/5/p1473-kosnita-theorem-triangle-circumcenter-concurrent-geogebra-1.jpg) |
Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration. |
![Dynamic Geometry 1469](../school-college/5/p1469-triangle-inradius-circumradius-midpoint-geogebra-1.jpg) |
Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration. |
![Dynamic Geometry 1468](../school-college/5/p1468-steiner-theorem-triangle-inradius-exradius-circumradius-ipad-geogebra-1.jpg) |
Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration. |
![Geometry Problem 1457](../school-college/5/p1457-orthocenter-triangle-similarity-circles-radii-1.jpg) |
Geometry
Problem 1457.
Altitudes, Circles, Similarity,
Product of the Inradii Lengths,
iPad. Step-by-step illustration using GeoGebra. |
![Geometry Problem 1456](../school-college/5/p1456-orthocenter-triangle-similarity-circles-geogebra-ipad-1.jpg) |
Geometry
Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area,
iPad. Step-by-step illustration using GeoGebra. |
![Problem 1443](../school-college/5/p1443-triangle-area-incenter-90-degree-circumcenter-1.jpg) |
Geometry Problem 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third
Area, Art, Poster, Typography, iPad Apps. |
![Problem 1438](../school-college/5/p1438-triangle-incenter-circuncenter-centroid-parallel-90-degree-ipad-apps-1.jpg) |
Geometry Problem 1438.
Triangle, Incenter, Centroid, Circumcenter, Parallel, 90 Degree, Art, Poster, Typography, iPad Apps. |
![Problem 1431](../school-college/5/p1431-apollonius-llc-triangle-circumcircle-tangent-congruent-angle-1.jpg) |
Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. |
![Problem 1423](../school-college/5/p1423-triangle-equal-angle-similarity-area-1.jpg) |
Geometry Problem 1423. Triangle, Area, Three Equal Angles, Circumradius, Measurement. |
![Problem 1419](../school-college/5/p1419-triangle-incenter-inradius-circumcircle-distance-sketch-ipad-1.jpg) |
Geometry Problem 1419. Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint. |
![Problem 1418](../school-college/5/p1418-triangle-incenter-parallel-angle-circle-tangent-1.jpg) |
Geometry Problem 1418. Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle. |
![Problem 1417](../school-college/5/p1417-triangle-incenter-circumcircle-tangent-cevian-bisector-perpendicular-1.jpg) |
Geometry Problem 1417. Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles. |
![Problem 1399](../school-college/4/p1399-triangle-circumcircle-perpendicular-angle-congruence-1.jpg) |
Geometry Problem 1399.
Triangle, Circumcircle, Perpendiculars, Angles, Congruence, Cyclic Quadrilateral. |
![Problem 1391](../school-college/4/p1391-triangle-ratio-area-circumcircle-1.jpg) |
Geometry Problem 1391. Two Triangles, Ratio of Areas, Circumcircle. |
![Problem 1388 Circle, Triangle](../school-college/4/p1385-triangle-circumcircle-orthocenter-bisector-collinear-1.jpg) |
Geometry Problem 1385. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. |
![Problem 1388 Circle, Triangle](../school-college/4/p1384-triangle-circumcircle-orthocenter-bisector-90-degree-1.jpg) |
Geometry Problem 1384. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree. |
![Geometry problem 1359](../school-college/4/p1359-triangle-circumcircle-equal-angle-midpoint-tutor-1.jpg) |
Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints. |
![Geometry problem 1347](../school-college/4/p1347-equilateral-triangle-bisector-circle-tangent-tutoring-1.jpg) |
Geometry Problem 1347. Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle. |
![Geometry problem 1341](../school-college/4/p1341-isosceles-triangle-80-20-80-bisector-circumcenter-1.jpg) |
Problem 1341.
Geometry Problem 1341: Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.
|
![Geometry problem 1337](../school-college/4/p1337-parallelogram-circumcircle-tangent-congruence-tutoring-1.jpg) |
Problem 1337.
Parallelogram, Diagonals, Circle, Circumcircle, Tangent Line, Triangle, Congruence.
|
![Geometry problem 1322](../school-college/4/p1322-triangle-bisector-circle-sum-angle-1.jpg) |
Geometry Problem 1322.
Triangle, Angle Bisector, Circumcircle, Chord, Secant, Sum of two Angles. |
![Geometry problem 1319](../school-college/4/p1319-hexagon-square-midpoint-equilateral-triangle-1.jpg) |
Geometry Problem 1319.
Hexagons, Equilateral Triangles, Center, Midpoints. |
![Geometry problem 1312](../school-college/4/p1312-triangle-60-degrees-circumcenter-orthocenter-measurement-1.jpg) |
Geometry Problem 1312.
Triangle, 60 Degrees, Circle, Circumcenter, Orthocenter, Altitude, Distance, Perpendicular, Measurement. |
![Geometry problem 1311](../school-college/4/p1311-triangle-circle-concyclic-measurement-1.jpg) |
Geometry Problem 1311.
Inscribed Triangle, Circle, Circumcircle, Concyclic Points, Measurement. |
![Geometry problem 1305](../school-college/4/p1305-triangle-angle-bisector-circumcircle-perpendicular-area-1.jpg) |
Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area. |
![Geometry problem 1277](../school-college/3/p1277-equilateral-triangle-externally-tangent-circle-tutoring-1.jpg) |
Geometry Problem 1277.
Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement. |
![Geometry problem 1276](../school-college/3/p1276-equilateral-triangle-internally-tangent-circle-tutoring-1.jpg) |
Geometry Problem 1276.
Equilateral Triangle, Circumcircle, Internally Tangent Circles, Tangent Line, Measurement. |
![Geometry problem 1274](../school-college/3/p1274-isosceles-triangle-80-20-80-measurement-1.jpg) |
Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement. |
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| by Antonio Gutierrez
Last updated: Feb 18, 2024
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