Geometría Plana: Líneas Concurrentes, Teoremas y Problemas

Problemas de Geometría
Problemas del 1301 al 1400
Problemas del 1201 al 1300
Problemas del 1101 al 1200
Problemas del 1001 al 1100

Problema de Geometria 630: Punto de Clawson.
Triangulo órtico, Extangencial, Homotecia, Líneas Concurrentes, Semejanza

Teorema de Kosnita.
Circuncentros, Líneas Concurrentes.

Punto de Fermat.
 

Punto de Vecten Exterior.
 

Teorema de Brianchon en un Hexágono Circunscrito.

Corolario de Brianchon, Hexágono Circunscrito, Líneas Concurrentes.

Teorema de las Isogonales de Jacobi
Usando TracenPoche, Software de Geometría Dinámica.

Problema de Geometría  730.
Triangulo, Altura, Ortocentro, Perpendicular, Líneas Concurrentes.

Problema de Geometría 728.
Triangulo, Altura, Perpendicular, Circumcirculo, Punto medio, Circunferencias secantes, Líneas Concurrentes.

Problema de Geometría 714.
Triangulo, Paralela, Ceviana, Punto medio, Mediana, Teorema de Ceva

Problema de Geometría 684: Outer Nagel Point.
Triangle, Excircles, Incircle Tangency points, Líneas Concurrentes, Semi-perimeter, Ceva theorem.

Problema de Geometría 683: Nagel Point.
Triangle, Excircles, Tangency points, Líneas Concurrentes, Semi-perimeter, Ceva theorem.

Problema de Geometría 682: Gergonne External Point.
Triangle, Excircle, Tangency points, Líneas Concurrentes, Semiperimeter, Ceva theorem.

Problema de Geometría 681: Gergonne Point.
Triangle, Incircle, Tangency points, Líneas Concurrentes, Semiperimeter, Ceva theorem.

Problema de Geometría 663.
Scalene Triangle, 60 Degrees, Altitude, Angle Bisector, Perpendicular Bisector, Líneas Concurrentes.

Problema de Geometría 656.
Triangle, Cevian, Líneas Concurrentes.

Problema de Geometría 625
Triangle, Parallel Lines, Congruence, Angle Bisector, Líneas Concurrentes.

Problema de Geometría 592.
Triangle, Incenter, Incircle, Tangency Point, Midpoints, Líneas Concurrentes, Congruence.

Problema de Geometría 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

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

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

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

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

Problema 404.
External Equilateral triangles, Congruent and Líneas Concurrentes.

Problema 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Problema 392.
Triangle, Parallel lines, Líneas Concurrentes.

Problema 390.
Triangle, Parallel lines, Collinear points.
Líneas Concurrentes.

Problema 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.
Líneas Concurrentes.

Problema 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.
Líneas Concurrentes.

Problema 345.
Equal circles, Tangents, Líneas Concurrentes, Hexagon, Semiperimeter.

Problema 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Problema 319.
Triangle, Altitudes, Perpendiculars, Collinear points.
Líneas Concurrentes.

Problema 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.

Problema 292.
Triangle, Parallel, Congruence, Similarity.

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

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

Problema 253.
Triangle, Centroid, Vertices, Distances, Squares.
Concurrent medians.

Problema 249.
Triangle sides, medians, squares.
Concurrent medians.

Problema 191. Triangle, Altitudes, Orthocenter, Squares, Areas.
Concurrent altitudes.

Problema 153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.  

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

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

Problema 136. Orthic Triangle, Concurrent Altitudes, Perpendicular, Concyclic Points.  

Problema 135. Orthic Triangle, Concurrent Altitudes, Perpendicular, Parallel  

Problema 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.
Líneas Concurrentes.

Problema 131. Van Aubel Theorem, Concurrent Cevians, Sum of Ratios.

Problema 130. Triangle, Concurrent Cevians, Sum of Ratios.

Problema 129. Triangle, Concurrent Cevians, Sum of Ratios.

Problema 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.
Líneas Concurrentes.

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.

Problema 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.
Líneas Concurrentes.

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

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

Seven Circles Theorem
Líneas Concurrentes of tangency points.

Triangle and Squares 22
Concurrent altitudes. 

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

Spieker Center
Líneas Concurrentes.

Second Ajima-Malfatti Point
Interactive illustration. Líneas Concurrentes.

First Ajima-Malfatti Point
Animated illustration. Líneas Concurrentes.

Triangle and Squares 17
Líneas Concurrentes.

Triangle and Squares 16
Líneas Concurrentes.

Blanchet Theorem
Líneas Concurrentes.

Steiner Point
 

Mittenpunkt Point
 

Problema 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.