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Geometric Mean, Theorems and Problems - Table of Content

Geometric Mean Index, theorems and problems

 

Geometric, Arithmetic, Harmonic Mean Relationship

Arithmetic Mean, Geometric Mean, Harmonic Mean, Root Mean Square.

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, catheti (legs), semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.

Archimedes' Book of Lemmas: Proposition 4
Semicircles, perpendicular to diameter, Arbelos. Geometric Mean.

Problem 1436

Geometry Problem 1436.
Right Triangle, Altitude, Excircles, Excenters, Geometric Mean, Measurement, Art, Poster, Typography, iPad Apps.

Problem 1434

Geometry Problem 1434.
Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement, Poster, Typography, iPad Apps.

Geometry Problem 1111

Geometry Problem 1111.
Right Triangle, External Squares, Cathetus, Angle Bisector, Area, Geometric Mean.

Geometry Problem 1105

Geometry Problem 1105.
Triangle, Incircle, Excircle, Cevian, Tangent, Congruence, Geometric Mean.

Geometry Problem 1103

Geometry Problem 1103.
Right Triangle, Incircle, Inscribed Circle, Radius, Geometric Mean, Sangaku, Japanese, Metric Relations.

Geometry Problem 1095

Geometry Problem 1095.
Externally Tangent Circles, Common Tangent, Radius, Metric Relations.

Geometry Problem 1020

Geometry Problem 1020.
Circle, Tangent, Chord, Perpendicular, Geometric Mean.

Geometry Problem 1009

Geometry Problem 1009.
Tangent Circles, Common External Tangent, Common Internal Tangent, Arithmetic Mean.

Geometry Problem 959

Geometry Problem 959.
Triangle, Sides Ratio 4:1, Inradius, Exradius, Cevian, Mean Proportional, Geometric Mean, Metric Relations.

Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional

Geometry Problem 834
Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional.

Tangent Circles, Geometric Mean

Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean.

Three Tangent Circles

Proposed Problem 315.
Three Tangent circles, Common external tangent line, Geometric Mean.

Tangent circles and line

Proposed Problem 314.
Tangent circles, Common external tangent line, Geometric Mean.

Circle, Chord, Tangent, Perpendicular

Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.

Right triangle, Altitude, perpendiculars

Proposed Problem 269.
Right Triangle, Altitude, Perpendicular, Projection, Geometric Mean.

Right triangle, Altitude, Geometric Mean

Proposed Problem 266.
Right Triangle, Altitude, Geometric Mean.

Right triangle

Geometry Problem 264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean.

Right triangle, inradius, altitude, arithmetic mean

Geometry Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.

Right triangle, inradius, altitude, arithmetic mean

Geometry Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.

Rhomus problem

Geometry Problem 219. Rhombus, Perpendiculars, Arithmetic Mean.

Problem 66: Triangle, Excircle, Tangents, Geometric Mean.
 

Right triangle, altitude, incircle, inradii

Problem 20.
Right triangle, altitude, incircles and inradii.

Perpendicular Chords

Perpendicular Chords. Index.
Theorems and Problems.

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Last updated: May 28, 2019 by Antonio Gutierrez