

Circumcenter, Circumcircle, Circumradius of a triangle, Geometry, Theorems and Problems
4


Circumcenter/Circumcircle 
Index 4




Geometry Problem 892
Triangle, 60 degrees, Orthocenter, Circumcenter. 

Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets. 

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. 

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.
StepbyStep 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.
StepbyStep 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 NinePoint Circle with interactive
animation, manipulation, and stepbystep construction.


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

Spieker Center 

Interactive Gergonne Line and Nobbs Points.
Circumcenter of the contact triangle.
Dynamic Geometry.
StepbyStep 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 

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. 
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 By Antonio Gutierrez






