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Circumcenter, Circumcircle, Circumradius of a triangle, Geometry, Theorems and Problems
4
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Circumcenter/Circumcircle -
Index 4
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Geometry Problem 892
Triangle, 60 degrees, Orthocenter, Circumcenter. |
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Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets. |
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Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence. |
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Geometry Problem 847
van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points. |
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Geometry Problem 846
Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral, Similarity. |
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Geometry Problem 845
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity. |
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Geometry Problem 844
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity. |
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Geometry Problem 843
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Parallel, Congruence, Similarity. |
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Geometry Problem 842
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity. |
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Geometry Problem 841
Triangle, Medians, Centroid, Circumcenters, Perpendicular, Congruence, Similarity. |
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Geometry Problem 837
Triangle, Orthocenter, Circumcenter, Circle, Concyclic Points. |
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Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity. |
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Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter. |
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Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle. |
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Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence. |
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Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance. |
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Geometry Problem 774
Triangle, Two Altitudes, Circumcircle, Tangent at a Vertex, Parallel. |
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Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement. |
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Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence. |
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Geometry Problem
742.
Scalene Triangle, Orthocenter, Centroid, Circumcenter, Circumradius, Midpoint, Distance, Square, Metric Relations. |
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Geometry Problem
741.
Scalene Triangle, Incenter, Circumcircle, Midpoint, Arc, Congruence. |
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Geometry Problem
733.
Triangle, Orthocenter, Altitude, Reflection in a line, Circumcircle, Concurrency. |
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Geometry Problem
729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Midpoint. |
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Geometry Problem
728.
Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency. |
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Geometry Problem
706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral. |
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Geometry Problem 675.
Circumcircles,
Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points. |
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Geometry Problem 670.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter,
Circumcircle Congruence. |
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Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map. |
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Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter,
Circumcircle, Angles,
Triangle centers. |
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Geometry Problem 662.
Triangle, Incenter, Circumcenter, Circumcircle, Orthocenter, Circle, Angle, Measurement. |
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Geometry Problem
586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency. |
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Geometry Problem
593.
Triangle, Circumcircle, Collinear Points. |
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Problem
585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency. |
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Problem
584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms. |
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Problem
583.
Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelogram, Octagon, Areas. |
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Problem
548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points,
Similarity. |
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Problem
547.
Triangle, Transversal, Four Circumcircles, Circumcircles, Concurrency. |
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Problem
538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint. |
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Problem
535.
Sawayama - Thebault's theorem: Triangle, Incircle, Circle, Circumcircle, Center, Tangent,
Collinear. |
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Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area. |
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Problem 526.
Equilateral Triangle, Circumcircle, Chord, Measurement. |
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Problem 476.
Triangle, Circumcenter, Circumcircle, Angles. |
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Proposed Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius,
Circumcenter, Circumcircle. |
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Proposed Problem 426.
Triangle, Circumradius, Circumcenter,
Circumcircle, concurrent Cevians. |
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Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector,
Congruence.
Puzzle
based on poblem 401. |
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Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear. |
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Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles. |
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Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points. |
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Puzzle: Euler Line and Nine Point Center
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Schiffler Point: Four Euler Lines with interactive animation and
manipulation.
Circumcenter, Circumcircle, Centroid, Orthocenter, and Incenter. |
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Interactive Simson Line. Dynamic
Geometry.
Step-by-Step construction, Manipulation, and animation.
Circumcenter O. |
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Angle between two
Simson Lines. Proof with animation.
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Simson Line. A proof
of Simson line with animation. |
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Triangle, Three Medians, Six Concyclic Circumcenters.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
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Proposed Problem 209. Circumcenter of the contact triangle.
Triangle, Incircles, Inradius. |
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Journey
to the Center of a Triangle (1976). Incenter, Circumcenter,
Centroid, Orthocenter. |
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Feuerbach Points and Nine-Point Circle with interactive
animation, manipulation, and step-by-step construction.
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Feuerbach
Point Facts.
Distances between Feuerbach point and the incenter,
nine-point center, centroid, Spieker point, and
Circumcenter |
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Spieker Center |
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Interactive Gergonne Line and Nobbs Points.
Circumcenter of the contact triangle.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation. |
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Steiner Point
Circumcenter, Lemoine Point. |
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Symmedian (Lemoine) Point
Triangle Center |
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Sangaku Problem (An Old Japanese Theorem).
Inradii, Carnot's theorem. |
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Carnot Theorem.
Circumcenter, circumradius, inradius |
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Steiner Theorem.
Circumcenter, circumradius, inradius,
exradii |
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Right Triangle: Circumcenter. Centers, Inradius, Circumradius,
Incenter, Circumcenter, Orthocenter, Centroid, Poncelet's theorem,
Sagitta. |
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Proposed Problem 160. Triangle,
Incircle, Incenter, Circumcircle, Circumcenter, Inradius. |
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Proposed Problem 159. Distances
from the Circumcenter to the Incenter and the Excenters. |
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Proposed Problem 158.
Circumcenter
Relation between the Circumradius, Inradius and Exradii of a triangle.
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Proposed Problem 157. Distance
from the Circumcenter to the Excenter. |
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Proposed Problem 156.
Circumcenter
Triangle, Circumradius, Exradius, Chord, Secant line. |
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Proposed Problem 155. Euler's
Theorem: Distance from the Incenter to the Circumcenter. |
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Proposed Problem 154.
Circumcenter.
Triangle, Inradius, Circumradius, Chord. |
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Proposed Problem 145. Four
Triangles, Incircle, Tangent and Parallel to Side, Incenters,
Circumcenters. |
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Proposed Problem 143.
Circumcenter.
Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii. |
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Proposed Problem 139.
Circumcenter.
Triangle Area, Orthic Triangle, Semiperimeter, Circumradius. |
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| By Antonio Gutierrez
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