Online Geometry: Concurrent Lines, Theorems and Problems

Concurrent Lines, Theorems and Problems - Table of Content

Clawson Point.
Orthic and Extangents Triangles, Concurrent lines.

Kosnita's Theorem.
Circumcenters, Concurrent lines.

Fermat Point.
 

Vecten Outer Point.
 

Brianchon's Theorem in a Circumscribed Hexagon.

Brianchon Corollary, Circumscribed Hexagon, Concurrency lines.

Geometry Problem 714.
Triangle, Parallel, Cevians, Midpoints, Median, Ceva Theorem.

Geometry Problem 684: Outer Nagel Point.
Triangle, Excircles, Incircle Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 683: Nagel Point.
Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 682: Gergonne External Point.
Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Geometry Problem 681: Gergonne Point.
Triangle, Incircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Geometry Problem 663.
Scalene Triangle, 60 Degrees, Altitude, Angle Bisector, Perpendicular Bisector, Concurrent lines.

Geometry Problem 656.
Triangle, Cevian, Concurrent Lines.

Geometry Problem 625
Triangle, Parallel Lines, Congruence, Angle Bisector, Concurrent lines.

Geometry Problem 592.
Triangle, Incenter, Incircle, Tangency Point, Midpoints, Concurrent Lines, Congruence.

Geometry Problem 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Problem 585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.

Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle.

Problem 479.
Triangle, Cevians, Concurrency, Transversal, Proportion.

Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity.

Proposed Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 392.
Triangle, Parallel lines, Concurrent lines.

Proposed Problem 390.
Triangle, Parallel lines, Collinear points.
Concurrent lines.

Proposed Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.
Concurrent lines.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.
Concurrent lines.

Proposed Problem 345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter.

Proposed Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Proposed Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.
Concurrent lines.

Proposed Problem 318.
A Scalene triangle, Altitudes, Collinear points.
Concurrent altitudes.

Excenter. Index.
Concurrent angle bisectors

Circumcenter. Index.
Concurrent perpendicular bisectors.

Orthocenter Index.
Concurrent altitudes.

Centroid /Barycenter. Index.
Concurrent medians.

Triangle Centers.

Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity.

Proposed Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Concurrent medians.

Proposed Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Concurrent medians.

Proposed Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.
Concurrent medians.

Proposed Problem 249.
Triangle sides, medians, squares.
Concurrent medians.

Proposed Problem 191. Triangle, Altitudes, Orthocenter, Squares, Areas.
Concurrent altitudes.

Proposed Problem 153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.  

Proposed Problem 138. Nagel's Theorem, Orthic Triangle, Concurrent Altitudes, Circumradius, Perpendicular.  

Proposed Problem 137. Orthic Triangle, Concurrent Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram.  

Proposed Problem 136. Orthic Triangle, Concurrent Altitudes, Perpendicular, Concyclic Points.  

Proposed Problem 135. Orthic Triangle, Concurrent Altitudes, Perpendicular, Parallel  

Proposed Problem 134. Orthic Triangle, Concurrent Altitudes, Angle Bisectors, Orthocenter, Incenter.  

Triangle, Medians, Six Circumcenters Concyclic. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Concurrent medians..

Trapezoid, Triangle, Diagonals, Midpoints. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Concurrent lines.

Proposed Problem 131. Van Aubel Theorem, Concurrent Cevians, Sum of Ratios.

Proposed Problem 130. Triangle, Concurrent Cevians, Sum of Ratios.

Proposed Problem 129. Triangle, Concurrent Cevians, Sum of Ratios.

Proposed Problem 128. Incenter of a Triangle, Concurrent Angle Bisectors, Sum of Ratios.

Triangle and Squares Theorem 1: with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Concurrent lines.

Gergonne's Theorem: Triangle and Concurrent Cevians.

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.

Proposed Problem 79: Triangle. Similarity, Concurrent Altitudes, Orthocenter, Incircles, Inradii.

Interactive Orthopole of a Triangle: Using TracenPoche Dynamic Geometry Software, Online Step-by-Step construction, manipulation, and animation.
Concurrent perpendiculars.

Schiffler Point: Concurrent Four Euler Lines with interactive animation and manipulation.

Van Aubel's Theorem II: Triangle and Concurrent Cevians.
 

Incenter, Excenter, Incircle, Excircle Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Concurrent angle bisectors.

Three Tangent Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Concurrent common tangent lines

Three Circles Theorem Using TracenPoche Dynamic Software.
Concurrent common chords

Isogonic-Jacobi Theorem: Using TracenPoche Dynamic Geometry Software.
Concurrent lines.

Marion Walter's Theorem: Triangle and Hexagon areas: Using TracenPoche Dynamic Geometry Software. Concurrent Lines?

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
Concurrent altitudes, median, perpendicular bisectors.

Seven Circles Theorem
Concurrent lines of tangency points.

Triangle and Squares 22
Concurrent altitudes. 

Proposed Problem 51: Fagnano's Problem
Inscribed Triangle with the Minimum Perimeter.
Concurrent altitudes.

Spieker Center
Concurrent lines.

Second Ajima-Malfatti Point
Interactive illustration. Concurrent lines.

First Ajima-Malfatti Point
Animated illustration. Concurrent lines.

Triangle and Squares 17
Concurrent lines.

Triangle and Squares 16
Concurrent lines.

Blanchet Theorem
Concurrent lines.

Steiner Point
 

Mittenpunkt Point
 

Proposed problem 21
Acute triangle, orthocenter, diameter, tangents. Concurrent altitudes.

Symmedian (Lemoine) Point
Triangle Center

Nagel Point Theorem. Proof.
Concurren lines. 

Gergonne Point Theorem. Concurrency. Interactive proof with animation.
Key concept: Ceva's Theorem.
 

The Bevan Point The circumcenter of the excentral triangle. Illustration with animation.
Concurrent perpendiculars.

Ceva's Theorem. Concurrency. Interactive proof with animation. Key concept: Menelaus Theorem.