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Points, Theorems and Problems - Index.
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Perpendicular
Bisector. |
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Butterfly Theorem
Proof with animation.
Midpoint of a chord. |
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Median of a Trapezoid, Theorems and Problems.
Index.
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Newton's
Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of
diagonals, center of the circle inscribed.
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GeoGebra, Dynamic Geometry:
Nine Point Circle
HTML5 Animation for Tablets (iPad, Nexus..) |
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GeoGebra, Dynamic Geometry:
Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..) |
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Equilic Quadrilateral.
120 degrees. Midpoints. |
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Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
Midpoints. |
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Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.
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Median
length, Apollonius' Theorem
Midpoints. |
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Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
Midpoints. |
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Symmedian (Lemoine)
Point
Triangle Center |
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Archimedes' Book of Lemmas:
Proposition 7
Square and inscribed and circumscribed Circles
Midpoints.
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Archimedes' Book of Lemmas:
Proposition 2
Semicircle, diameter, tangents, secant line.
Midpoint. |
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Archimedes' Book of Lemmas:
Proposition 3
Semicircle, perpendicular to diameter, chords.
Midpoint. |
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Archimedes' Book of Lemmas:
Proposition 10
Tangents to a circle, secant line and chords, Parallel.
Midpoint. |
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Archimedes' Book of Lemmas:
Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Midpoint,
Perpendicular, Radius. |
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Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Midpoints. |
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Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.
Perpendiculars from the midpoints. |
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Marion
Walter's Theorem: Triangle and Hexagon areas:
Using TracenPoche Dynamic Geometry Software.
Midpoints. |
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Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
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Mascheroni
Construction with compass alone. Midpoint of a segment.
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Heron's Formula with medians.
Midpoints. |
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Mittenpunkt Point
Midpoints. |
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Dynamic Geometry: Brahmagupta Theorem,
. GeoGebra, HTML5 Animation for Tablets |
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Geometry Problem 1575:
Prove an Angle Bisector in a Triangle Involving an Altitude, Midpoint, and Excircle |
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Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
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Geometry Problem 1563:
Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
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Geometry Problem 1562:
Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint. |
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Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. |
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Geometry Problem 1559:
Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels. |
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Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. |
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Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence |
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Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC |
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Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors |
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Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes |
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Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc. |
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Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!. |
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Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. |
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Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. |
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Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
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Geometry
Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. |
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Geometry
Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. |
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Geometry
Problem 1523 and a Thematic Poem.
Discover How to Calculate the Length of the Altitude in an Isosceles Triangle - Get Expert Geometry Tips Now!
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Geometry
Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. |
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Geometry
Problem 1519 and a Thematic Poem.
Discover the Length of a Segment in a Parallelogram using Midpoints and Parallel Lines. |
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Geometry
Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School. |
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Geometry
Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School. |
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Geometry
Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School. |
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Geometry
Problem 1494.
Parallelogram, Midpoints, Octagon, Areas. |
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Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration. |
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Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration. |
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Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. |
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Dynamic Geometry
1460.
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals,
Collinear Points, Step-by-step Illustration using GeoGebra. |
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Geometry
Problem 1459.
Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra. |
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Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra. |
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Geometry Problem 1429.
Triangle, Median, 15-30 degree, Angle, Congruence. |
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Geometry Problem 1417.
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles, Midpoint. |
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Geometry Problem 1408.
Right Triangle, Incircle, Excircle, Incenter, Midpoint, Tangency Point, Collinearity. |
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Geometry Problem 1395.
Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency. |
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Geometry Problem 1385.
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. |
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Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps. |
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Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps. |
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Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints. |
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Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments. |
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Geometry Problem 1351.
Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. |
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Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.
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Problem 1336.
Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.
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Geometry Problem 1325.
Octagons, Midpoints, Squares, Mobile Apps, iPad. |
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Geometry Problem 1317.
Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence. |
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Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence. |
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Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence. |
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Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. |
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Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint. |
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Geometry Problem 1294.
Triangle, Altitudes, Four Squares, Center, Midpoint, Concyclic Points. |
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Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint. |
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Geometry Problem 1291.
Three Squares, Collinear Vertices, Midpoint, Congruence. |
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