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Geometry, Concurrent Lines, Theorems and Problems
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Concurrent Lines - Table of Content
- Page 1
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![Concurrent lines, Index](concurrent_lines_index_17.jpg) |
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![Clawson Point](../center/clawson_point_triangle_1.jpg) |
Clawson Point.
Orthic and Extangents Triangles, Concurrent lines. |
![Kosnita theorem](../center/kosnita_theorem_17.jpg) |
Kosnita's Theorem.
Circumcenters, Concurrent lines. |
![Fermat Point](../center/fermat_point_1.jpg) |
Fermat Point.
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![Vecten Point](../center/vecten_point_1.jpg) |
Vecten Outer Point.
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![Brianchon Theorem](brianchon_theorem_hexagon_1.jpg) |
Brianchon's Theorem in a Circumscribed Hexagon. |
![Brianchon Corollary](brianchon_corol_hexagon_1.jpg) |
Brianchon Corollary, Circumscribed Hexagon, Concurrency lines. |
![Isogonic-Jacobi Theorem](isogonic_jacobi_theorem_1.jpg) |
Isogonic-Jacobi
Theorem
Using TracenPoche Dynamic Geometry Software |
![Geometry Problem 1498](../school-college/5/p1498-intersecting-circles-diameter-common-chord-secant-cyclic-quadrilateral-concyclic-collinear-points-1.jpg) |
Geometry
Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points. |
![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 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 1471](../school-college/5/p1471-equilateral-triangle-incenter-concurrent-geogebra-ipad-1.jpg) |
Dynamic Geometry 1471.
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration. |
![Dynamic Geometry 1451](../school-college/5/p1451-orthopole-geogebra-triangle-perpendicular-concurrency-1.jpg) |
Dynamic Geometry 1451.
Orthopole of a Line. Step-by-step
illustration using GeoGebra. |
![Problem 1425](../school-college/5/p1425-two-squares-concurrent-lines-1.jpg) |
Geometry Problem 1425. Two Squares, Collinear Points, Concurrent Lines. |
![Problem 1400](../school-college/4/p1400-triangle-rectangles-perpendicular-bisector-concurrency-1.jpg) |
Geometry Problem 1400. Triangle with three rectangles on the sides, Perpendicular Bisectors, Concurrency. |
![Problem 1396](../school-college/4/p1396-triangle-rectangles-perpendicular-concurrency-1.jpg) |
Geometry Problem 1396. Triangle with three rectangles on the sides, Vertices, Perpendicular lines, Concurrency. |
![Problem 1395](../school-college/4/p1395-triangle-rectangles-midpoints-concurrency-1.jpg) |
Geometry Problem 1395. Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency. |
![Problem 1394](../school-college/4/p1394-three-circles-common-internal-tangent-concurrent-1.jpg) |
Geometry Problem 1394. Three Circles and Three Pair of Common Internal Tangents, Concurrency. |
![Geometry problem 1301](../school-college/4/p1301-arbelos-incircle-square-midpoint-1.jpg) |
Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. |
![Geometry problem 1300](../school-college/3/p1300-arbelos-incircle-tangent-bisector-concurrency-1.jpg) |
Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines. |
![Geometry problem 1293](../school-college/3/p1293-triangle-square-altitude-concurrent-1.jpg) |
Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint. |
![Geometry problem 1289](../school-college/3/p1289-triangle-concurrent-cevian-measurement-1.jpg) |
Geometry Problem 1289.
Triangle, Cevian, Concurrency, Measurement, Metric Relations. |
![Geometry problem 1264](../school-college/3/p1264-triangle-exterior-angle-bisector-90-degree-concurrent
-1.jpg) |
Geometry Problem 1264.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1260](../school-college/3/p1260-triangle-angle-bisector-90-degree-concurrent-1.jpg) |
Geometry Problem 1260.
Triangle, Internal Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1253](../school-college/3/p1253-triangle-orthocenter-90-degree-circles-1.jpg) |
Geometry Problem 1253.
Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency. |
![Geometry problem 1242](../school-college/3/p1242-quadrilateral-angle-bisector-collinearity-1.jpg) |
Geometry Problem 1242.
Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines. Mobile Apps. |
![Geometry problem 1237](../school-college/3/p1237-imo-2016-problem-1-triangle-parallel-concurrent-1.jpg) |
Geometry Problem 1237
IMO 2016, Problem 1, Triangle, Congruence, Parallel Lines, Midpoint, Concurrency. |
![Geometry problem 1235](../school-college/3/p1235-triangle-cevian-concurrent-circle-1.jpg) |
Geometry Problem 1235
Triangle, Cevians, Concurrency, Circle, Circumcircle. |
![Geometry problem 1212](../school-college/3/p1212-equilateral-triangle-inscribed-hexagon-concurrency-1.jpg) |
Geometry Problem 1212
Equilateral Triangle, Equilateral Hexagon, Concurrent Lines. |
![Geometry problem 1184](../school-college/2/p1184-right-triangle-square-circle-tangent-concurrent-1.jpg) |
Geometry Problem 1184
Right Triangle, Square, Inscribed Circle, Tangent, Concurrent Lines. |
![Geometry problem 1176](../school-college/2/p1176-cyclic-quadrilateral-circle-diameter-collinear-concurrent-1.jpg) |
Geometry Problem 1176
Cyclic Quadrilateral, Diagonals, Six Diameters, Circles, Collinear Points, Concurrent Lines. |
![Geometry problem 1141](../school-college/2/p1141-positive-geometry-pentagon-triangle-circle-concurrent-mindmap-1.jpg) |
Geometry Problem 1141.
Inscribed Pentagon, Circle, Triangle, Congruence, Midpoint, Concurrency. |
![Geometry problem 1139](../school-college/2/p1139-triangle-circumcircle-bisector-parallel-90-degrees-concurrent-1.jpg) |
Geometry Problem 1139.
Triangle, Circumcircle, Angle Bisector, Parallel Lines, 90 Degrees, Concurrent Lines. |
![Geometry Problem 1088](../school-college/1/p1088-triangle-perpendicular-concurrent-lines-tutoring-math-1.jpg) |
Geometry Problem
1088.
Triangles, Perpendicular, Concurrent Lines. |
![Geometry Problem 1047](../school-college/1/p1047-parallelogram-parallel-diagonal-concurrency-math-1.jpg) |
Geometry Problem
1047.
Parallelogram, Parallel Lines, Concurrent Lines, Diagonals. |
![Geometry Problem 1012](../school-college/1/p1012-equilateral-triangle-incenter-perpendicular-concurrent-math-1.jpg) |
Geometry Problem
1012.
Equilateral Triangle, Incenters, Inscribed Circles, Perpendicular, Concurrent Lines. |
![Geometry Problem 1007](../school-college/1/p1007-hexagon-midpoint-triangle-median-centroid-concurrent-math-1.jpg) |
Geometry Problem
1007.
Hexagon, Midpoint, Triangle, Median, Centroid, Concurrency. |
![Geometry Problem 1004](../school-college/1/p1004-triangle-squares-perpendicular-bisectors-concurrent-math-1.jpg) |
Geometry Problem
1004.
Triangle with Squares, Perpendicular Bisectors, Concurrent Lines. |
![Geometry Problem 994](../school-college/p994-trapezoid-midpoint-bases-concurrent-lines-1.jpg) |
Geometry Problem 994.
Trapezoid, Midpoints of the bases, Concurrent Lines. |
![Geometry Problem 981](../school-college/p981-triangle-cevian-concurrent-midpoint-hexagon-area-1.jpg) |
Geometry Problem 981.
Triangle, Concurrent Cevians, Midpoints, Area, Hexagon. |
![Geometry Problem 979](../school-college/p979-triangle-cevian-concurrency-angle-bisector-90-degrees-1.jpg) |
Geometry Problem 979.
Triangle, Cevian, Angle Bisector, Concurrency, 90 Degrees, Perpendicular. |
![Geometry Problem 974](../school-college/p974-cevian-triangle-reflection-concurrency-begonia-theorem-point-geogebra-1.jpg) |
Geometry Problem 974.
'Begonia Theorem', Cevian Triangle, Reflection of a point in a line, Concurrency of Lines. GeoGebra, HTML5 Animation for Tablets. |
![Geometry Problem 945](../school-college/p945-triangle-concurrent-lines-perpendicular-angle-bisector-1.jpg) |
Geometry Problem 945.
Triangle, Concurrent Lines, Cevians, Perpendicular, Angle Bisector. |
![Problem 929](../school-college/p929-triangle-orthocenter-reflection-circumcircle-concurrency-1.jpg) |
Geometry Problem 929.
Triangle, Orthocenter, Circumcircle, Reflection, Concurrency.
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![Problem 928](../school-college/p928-triangle-area-median-cevian-concurrency-1.jpg) |
Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.
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![Excenter, Excircle, Index](../center/excenter_excircle_17.jpg) |
Excenter. Index.
Concurrent angle bisectors
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![Circumcenter Index](../center/circumcenter_index_17.jpg) |
Circumcenter. Index.
Concurrent perpendicular bisectors.
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![Orthocenter Index](../center/orthocenter_altitude_index.jpg) |
Orthocenter
Index.
Concurrent altitudes.
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![Centroid of a triangle Index](../center/centroid_barycenter_index.jpg) |
Centroid /Barycenter. Index.
Concurrent medians. |
![Centers](http://gogeometry.com/triangle_center_170.jpg) |
Triangle Centers.
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![Elearning Geometry](triangle_median_circ_17.jpg) |
Triangle,
Medians, Six Circumcenters Concyclic.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Concurrent medians.. |
![Trapezoid](trapezoid_diagonal_01_17.jpg) |
Trapezoid,
Triangle, Diagonals, Midpoints.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Concurrent lines. |
![Triangle Square Theorem 1. Elearning, Online Tutoring](triangle_square_01_17.jpg) |
Triangle
and Squares Theorem 1: with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Concurrent lines. |
![Gergonne's theorem](gergonne_theorem_170.jpg) |
Gergonne's Theorem:
Triangle and Concurrent Cevians. |
![](taylor_circle_theorem.jpg) |
Taylor Circle Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Henry Martyn Taylor and the blind student of mathematics
Concurrent altitudes. |
![](orthopole_triangle_170.jpg) |
Interactive Orthopole of
a Triangle: Using TracenPoche Dynamic
Geometry Software, Online
Step-by-Step construction, manipulation, and animation.
Concurrent perpendiculars. |
![](schiffler_point_euler_17.jpg) |
Schiffler Point: Concurrent Four Euler Lines with interactive
animation and manipulation.
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![Van Aubel's theorem II](van_aubel_theorem_ii_17.jpg) |
Van Aubel's Theorem II:
Triangle and Concurrent Cevians.
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![](incenter_excenter_17.jpg) |
Incenter, Excenter, Incircle, Excircle Using TracenPoche Dynamic
Software
Step-by-Step construction, Manipulation, and animation.
Concurrent angle bisectors. |
![](three_tangent_circles_theo_.jpg) |
Three Tangent Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Concurrent common tangent lines |
![](three_circles_theorem_17.jpg) |
Three Circles Theorem
Using TracenPoche Dynamic Software.
Concurrent common chords |
![](../center/lemoine_point_170.jpg) |
Symmedian (Lemoine)
Point
Triangle Center |
![](../NagelPoint170.jpg) |
Nagel Point
Theorem. Proof.
Concurren lines. |
![Gergonne Point Theorem](../gergonne170x100.jpg) |
Gergonne Point Theorem. Concurrency.
Interactive proof with animation.
Key concept: Ceva's Theorem.
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![](../Bevan170.jpg) |
The Bevan Point The
circumcenter of the excentral triangle. Illustration with animation.
Concurrent perpendiculars.
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![Ceva's theorem](../ceva170x100.jpg) |
Ceva's Theorem.
Concurrency. Interactive proof with animation. Key concept:
Menelaus Theorem.
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Post a comment | Email | by Antonio Gutierrez
Last updated:
Mar 24, 2022
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