
Midpoint, Theorems and
Problems  Index (Page 1)




Points, Theorems and Problems  Index.


Perpendicular
Bisector. 

Butterfly Theorem
Proof with animation.
Midpoint of a chord. 

Median of a Trapezoid, Theorems and Problems.
Index.


Newton's
Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of
diagonals, center of the circle inscribed.


GeoGebra, Dynamic Geometry:
Nine Point Circle
HTML5 Animation for Tablets (iPad, Nexus..) 

GeoGebra, Dynamic Geometry:
Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..) 

Equilic Quadrilateral.
120 degrees. Midpoints. 

Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 18641933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
Midpoints. 

Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.


Median
length, Apollonius' Theorem
Midpoints. 

Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
Midpoints. 

Symmedian (Lemoine)
Point
Triangle Center 

Archimedes' Book of Lemmas:
Proposition 7
Square and inscribed and circumscribed Circles Midpoints.


Archimedes' Book of Lemmas:
Proposition 2
Semicircle, diameter, tangents, secant line.
Midpoint. 

Archimedes' Book of Lemmas:
Proposition 3
Semicircle, perpendicular to diameter, chords.
Midpoint. 

Archimedes' Book of Lemmas:
Proposition 10
Tangents to a circle, secant line and chords, Parallel.
Midpoint. 

Archimedes' Book of Lemmas:
Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Midpoint,
Perpendicular, Radius. 

Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
StepbyStep construction, Manipulation, and animation.
Midpoints. 

EightPoint Circle Theorem
StepbyStep construction, Manipulation, and animation.
Perpendiculars from the midpoints. 

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

NinePoint Center, NinePoint Circle, Euler Line.
Interactive illustration.


Mascheroni
Construction with compass alone. Midpoint of a segment.


Heron's Formula with medians.
Midpoints. 

Mittenpunkt Point
Midpoints. 

Dynamic Geometry: Brahmagupta Theorem,
. GeoGebra, HTML5 Animation for Tablets 

Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.


Problem 1336.
Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.


Geometry Problem 1325.
Octagons, Midpoints, Squares, Mobile Apps, iPad. 

Geometry Problem 1317.
Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence. 

Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence. 

Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence. 

Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. 

Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint. 

Geometry Problem 1294.
Triangle, Altitudes, Four Squares, Center, Midpoint, Concyclic Points. 

Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint. 

Geometry Problem 1291.
Three Squares, Collinear Vertices, Midpoint, Congruence. 
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