Teoremas y Problemas de Geometria, Pre-Universitaria, Bachillerato

Líneas Concurrentes, Teoremas y Problemas - Tabla de Contenido

Lineas Concurrentes, ESL 

Punto de Clawson

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

Teorema de Kosnita

Teorema de Kosnita.
Circuncentros, Líneas Concurrentes.

Fermat Point

Punto de Fermat.
 

Vecten Point

Punto de Vecten Exterior.
 

Brianchon Theorem

Teorema de Brianchon en un Hexágono Circunscrito.

Brianchon Corollary

Corolario de Brianchon, Hexágono Circunscrito, Líneas Concurrentes.

Isogonic-Jacobi Theorem

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

Triangle, Altitude, Perpendicular, Concurrent

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

Triangle, Circle, Concurrency

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

Triangle, Parallel, Concurrent, Ceva, Midpoint

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

Outer Nagel Point

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

Nagel Point

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

Gergonne Point Theorem

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

Gergonne Point Theorem

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

Triangle, 60 Degrees, Concurrent lines

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

Triangle, Cevian, Concurrent Lines

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

Triangle, Parallel, Angle Bisector

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

Triangle, Incircle, Inradius, Midpoint, Concurrency

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

Cyclic quadrilateral, Circumcenter, Concurrency

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

Cyclic quadrilateral, Circumcenter, Concurrency

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

Triangle, Cevian, Circle, Concurrency

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

Triangle COncurrency, Transversal, Proportion

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

Triangle area, parallel, concurrency

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

Equilateral triangles

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

Triangle, Orthocenter

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

Triangle, Parallel, Concurrent lines

Problema 392.
Triangle, Parallel lines, Líneas Concurrentes.

Triangle, Parallel, Collinear points

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

Triangle, 120 degrees, angle bisectors

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

Equilateral triangle, circumcircle

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

Geometry Problem: Equal circles, Tangents

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

Elearning 324: Quadrilateral

Problema 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Triangle, Altitude

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

Elearning 318

Problema 318.
A Scalene triangle, Altitudes, Collinear points.
Concurrent altitudes.

Excenter, Excircle, Index

Excenter. Index.
Concurrent angle bisectors

Circumcenter Index

Circumcenter. Index.
Concurrent perpendicular bisectors.

Orthocenter Index

Orthocenter Index.
Concurrent altitudes.

Centroid of a triangle Index

Centroid /Barycenter. Index.
Concurrent medians.

Centers

Triangle Centers.

Triangle, Parallel, Congruence, Similarity

Problema 292.
Triangle, Parallel, Congruence, Similarity.

Problem 254: Triangle and Centroid

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

Elearning 254: Triangle and Centroid

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

Elearning 253: Triangle, Centroid

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

Triangle sides, medians, squares

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

Geometry Problem 191 about triangle and squares

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

Circumscribed quadrilateral

Problema 153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.  

Nagel Theorem

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

Geometry Problem 137

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

Geometry Problem 136

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

Geometry Problem 135

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

Geometry Problem 134

Problema 134. Orthic Triangle, Concurrent Altitudes, Angle Bisectors, Orthocenter, Incenter.  

Elearning Geometry

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

Trapezoid

Trapezoid, Triangle, Diagonals, Midpoints. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Líneas Concurrentes.

Elearning 131: Van Aubel, Concurrent Cevians

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

Elearning 130: Concurrent Cevians

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

Elearning 129: Concurrent ceviasn, ratios

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

Elearn 128: Incenter, Ratios

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

Triangle Square Theorem 1. Elearning, Online Tutoring

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

Gergonne's theorem

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

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

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

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

Home | Search | Geometría | Líneas | Email | Publicar un comentario | By Antonio Gutierrez