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![Teoremas y Problemas de Geometria, Pre-Universitaria, Bachillerato](h_problemas_geometria_910.jpg)
Geometría Plana: Punto Medio, Teoremas y Problemas
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Teoremas y Problemas. |
![El Punto, Teoremas y Problemas, Indice](punto_teoremas_problemas_1.jpg) |
Puntos, Teoremas y Problemas
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![Mediatriz, Teoremas y Problemas](mediatriz_teoremas_i_1.jpg) |
Mediatriz de un Segmento.
Punto medio,
Teoremas y Problemas |
![](teorema-de-la-mariposa-circunferencia-esl-1.jpg) |
Teorema de la Mariposa
Demostración animada.
Punto medio de una cuerda. |
![Trapezoid median, Theorems and Problems, Index](../geometry/trapezoid_median_index_17.jpg) |
Mediana del Trapecio, Teoremas y Problemas
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![](../NewtonTheorem170.jpg) |
Teorema de Newton:
Recta de Newton. Cuadrilátero circunscrito, Puntos medios de las
diagonales, Centro de la circunferencia inscrita.
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![](cuadrilatero_equilico_i_1.jpg) |
Cuadrilátero Equílico.
60,
120 grados. Puntos medios. |
![](../Kurschak170x100.jpg) |
Teorema de Kurschak.
Jozsef Kurschak (Hungría, 1864-1933) Elegante forma de encontrar el área
de un dodecágono regular a partir de los puntos medios de los lados de
un cuadrado. |
![](../Varignon_Wittenbauer_170.jpg) |
Paralelogramos de Varignon y Wittenbauer. Cuadrilátero: Puntos medios y
trisección de los lados.
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![Median Length theorem](../geometry/median_length_17.jpg) |
Longitud de la Mediana, Teorema de Apolonio
Puntos medios. |
![Van Aubel](../vanaubel170x100.jpg) |
Teorema de van Aubel.
Cuadrilátero con cuadrados sobre sus lados. Demostración animada.
Puntos medios. |
![](../center/lemoine_point_170.jpg) |
Punto Simediano (Lemoine)
Puntos notables del triangulo |
![](../ArchBooLem07_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 7
Square and inscribed and circumscribed Circles Puntos medios.
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![](../ArchBooLem02_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 2
Semicircle, diameter, tangents, secant line.
Puntos medio. |
![](../ArchBooLem03_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 3
Semicircle, perpendicular to diameter, chords.
Puntos medio. |
![](../ArchBooLem10_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 10
Tangents to a circle, secant line and chords, Parallel.
Puntos medio. |
![](../ArchBooLem15_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Puntos medio,
Perpendicular, Radius. |
![Bottema Theorem. Elearning.](../geometry/bottema_theorem_elearning.jpg) |
Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Puntos medios. |
![Eight Point Circle Theorem. Elearning](../geometry/eight_point_circle_17.jpg) |
Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.
Perpendiculars from the Puntos medios. |
![](../geometry/marion_walter_theorem.jpg) |
Marion
Walter's Theorem: Triangle and Hexagon areas:
Using TracenPoche Dynamic Geometry Software.
Puntos medios. |
![](../center/nine_point_center_euler_170.jpg) |
Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
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![](../circle/mascheroni_construction_1.jpg) |
Mascheroni
Construction with compass alone. Puntos medio of a segment.
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![](../heron/heron_medians_170x100.jpg) |
Heron's Formula with medians.
Puntos medios. |
![](../center/mittenpunkt_point_170.jpg) |
Mittenpunkt Point
Puntos medios. |
![Scalene Triangle, Median, Perpendicular, Angle, Measurement](../school-college/p802-triangle-median-perpendicular-angle-1.jpg) |
Geometry Problem
802
Scalene Triangle, Median, Perpendicular, Angle, Measurement. |
![Equilateral Triangles, Midpoint](../school-college/p801-equilateral-triangle-metric-relation-1.jpg) |
Geometry Problem
801
Equilateral Triangles, Cevian, Puntos medio, Distance, Measurement, Metric Relations. |
![Right Triangle, Altitude, Incircles, CIrcumcircles, COngruence](../school-college/795-intersecting-circles-secant-chord-midpoint-90-degrees-1.jpg) |
Geometry Problem 795
Intersecting Circles, Common Chord, Puntos medio, Tangent, Secant Line, Perpendicular, 90 Degrees. |
![Regular Hexagon, Midpoints, Equilateral Triangle](../school-college/p791-regular-hexagon-midpoint-equilateral-triangle-area-1.jpg) |
Geometry Problem 791
Regular Hexagon, Puntos medios of Side and Diagonal, Equilateral Triangle, Area. |
![Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral](../school-college/p788-intersecting-circle-midpoint-cyclic-quadrilateral-1.jpg) |
Geometry Problem 788
Intersecting Circles, Secant Line, Puntos medio, Cyclic Quadrilateral. |
![Triangle, Orthocenter, Midpoint](../school-college/p784-triangle-orthocenter-midpoint-perpendicular-1.jpg) |
Geometry Problem 784
Triangle, Orthocenter, Puntos medio of a side, Perpendicular. |
![Triangle, Orthocenter, Circumcircle, Diameter, Midpoint](../school-college/p783-triangle-orthocenter-circumcircle-diameter-midpoint-1.jpg) |
Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude,
Puntos medio. |
![Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular](../school-college/p781-triangle-circumcenter-perpendicular-orthocenter-midpoint-1.jpg) |
Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Puntos medio, Perpendicular. |
![Triangle, Orthocenter, Midpoint, 90 Degrees](../problem/p779-triangle-altitude-orthocenter-midpoint-90-degrees-1.jpg) |
Geometry Problem 779
Triangle, Altitude, Orthocenter, Puntos medio, Angle, 90 Degrees. |
![Triangle, Isogonal lines, Congruent angles, Perpendicular](../problem/p776-triangle-isogonal-perpendicular-feet-concyclic-midpoint-1.jpg) |
Geometry Problem 776
Triangle, Isogonal lines, Congruent angles, Perpendicular, Concyclic points, Circle, Center,
Puntos medio. |
![Intersecting Circles, Midpoint, Secant, Bisection](../problem/p773-intersecting-circles-midpoint-secant-1.jpg) |
Geometry Problem 773
Intersecting Circles, Puntos medio, Secant line, Bisection. |
![Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations](../problem/p772-triangles-common-vertex-similarity-sas-midpoint-1.jpg) |
Geometry Problem 772
Similar triangles with a Common Vertex, Equal Angles, Puntos
medios, Metric relations. |
![Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint arc, Parallel chord, Congruence](../problem/p769-triangle-circumcenter-orthocenter-midpoint-arc-parallel-congruence-1.jpg) |
Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Puntos medio of arc, Parallel to chord, Congruence. |
![Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle](../problem/p762-parallelogram-midpoint-perpendicular-congruence-1.jpg) |
Geometry Problem 762
Parallelogram, Puntos medio, Perpendicular, Congruence, Isosceles triangle. |
![Equilateral triangle, Circumcircle, Midpoint](../problem/p755-equilateral-triangle-circumcircle-midpoint-perpendicular-1.jpg) |
Geometry Problem 755.
Equilateral Triangle, Circumcircle, Chord, Arc, Puntos
medios, Perpendicular. |
![Triangle, Orthocenter, Centroid, Circumcenter, Circumradius, Midpoint](../problem/p742-circumradius-orthocenter-centroid-midpoint-distance-1.jpg) |
Geometry Problem
742.
Scalene Triangle, Orthocenter, Centroid, Circumcenter, Circumradius,
Puntos medio, Distance, Square, Metric Relations. |
![Triangle, Incenter, Circumcircle](../problem/p741-triangle-incenter-circumcircle-midpoint-arc-chord-congruence-1.jpg) |
Geometry Problem
741.
Scalene Triangle, Incenter, Circumcircle, Puntos medio, Arc, Congruence. |
![Triangle, Median, Isosceles, Congruence, Parallel](../problem/p734_triangle_median_1.jpg) |
Geometry Problem
734.
Triangle, Isosceles, Median, Parallel, Angle Bisector, Congruence,
Puntos medio. |
![Triangle, Orthocenter, Circumcircle](../problem/p729_triangle_orthocenter1.jpg) |
Geometry Problem
729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular,
Puntos medio. |
![Isosceles Triangle, Perpendicular, Midpoint](../problem/p726_triangle_90_degrees_1.jpg) |
Geometry Problem
726.
Isosceles Triangle, Perpendicular, Puntos medio, 90 Degrees. |
![Kurschak Dodecagon](../problem/p725_kurschak_dodecagon_1.jpg) |
Geometry Problem
725.
Kurschak's Dodecagon, Square, Equilateral Triangle, Puntos
medios, 30, 60 Degrees. |
![Triangle, Parallel, Concurrent, Ceva, Midpoint](../problem/p714_triangle_parallel_1.jpg) |
Geometry Problem
714.
Triangle, Parallel, Cevians, Puntos medios, Median, Ceva Theorem. |
![Rectangle, Midpoint, Concyclic points](../problem/p711_rectangle_concyclic_1.jpg) |
Geometry Problem
711.
Rectangle, Puntos medio, Angle, Concyclic Points, Cyclic Quadrilateral. |
![Parallelogram, Midpoint, Diagonal, Collinear, Metric Relations, Similarity, Congruence](../problem/p710_parallelogram_metric_1.jpg) |
Geometry Problem
710.
Parallelogram, Puntos medio, Diagonal, Collinear Points, Metric Relations, Triangle, Similarity, Congruence. |
![Parallelogram, Midpoints, Diagonal](../problem/p709_parallelogram_metric_1.jpg) |
Geometry Problem
709.
Parallelogram, Puntos medio, Diagonal, Metric Relations, Triangle. |
![Orthocenter, triangle, midpoint, perpendicular](../problem/p704_orthocenter_triangle_1.jpg) |
Geometry Problem
704.
Triangle, Orthocenter, Altitude, Puntos medio, Perpendicular. |
![Triangle, Circle, Median, Proportion](../problem/p679-triangle-circle-1.jpg) |
Geometry Problem 679.
Triangle, Circle, Median, Proportion. |
![Parallelogram, Midpoint, Diagonal](../problem/p677-parallelogram-1.jpg) |
Geometry Problem 677.
Parallelogram, Puntos medio, Diagonal, Metric Relations. |
![Triangle, Circumcircle, Incenter](../problem/p669_triangle_incenter_1.jpg) |
Geometry Problem 669.
Triangle, Circumcircle, Incenter, Puntos medio, Collinear points, Mind Map. |
![Triangle, Angle Bisectors, Midpoint, Collinear](../problem/p632_triangle_collinear_1.jpg) |
Geometry Problem 632.
Triangle, Interior and Exterior Angle Bisectors, Puntos medios, Collinear Points. |
![Triangle, Incircle, Altitude, Incenter, Angle](../problem/p594_triangle_incircle_1.jpg) |
Geometry Problem
594.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Puntos medio, Altitude, Angle, Half the Difference. |
![Triangle, Incircle, Inradius, Midpoint, Concurrency](../problem/p592_triangle_incenter_1.jpg) |
Geometry Problem
592.
Triangle, Incenter, Incircle, Tangency Point, Puntos medios, Concurrent Lines, Congruence. |
![Triangle, Incircle, Inradius, Altitude, Midpoint](../problem/p591_triangle_incenter_1.jpg) |
Geometry Problem
591.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Puntos medio, Altitude. |
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