


Metric Relations in a Right Triangle, Theorems and Problems: Table of Content




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

The General Extension to Pythagoras' Theorem. 

The Pythagorean Curiosity
Triangles and squares, fifteen conclusions. 

Word Cloud of Pythagorean Theorem


Einstein and
Pythagoras theorem proof


Geoboard
for iPad Pythagorean Theorem Proof by Leonardo. 

Geometry Problem
800: de Gua's Theorem
Pythagorean theorem in 3D, Tetrahedron, Cubic Vertex, Triangular Pyramid, Apex, Height, Right Triangle Area, Base Area, Projected Area. 

Geoboard
for iPad Pythagorean Theorem Proof, Squares, (Problem 540). 

Pythagorean spiral or Square Root Spiral or Spiral of Theodorus. 

Geometry Problem
1022.
Circular Sector of 90 Degrees, Squares, Metric Relations. 

Geometry Problem
1013.
Square, Line through the Center, Perpendicular, Distance, Metric Relations. 

Geometry Problem 973.
Three Parallel, Square, Vertices, Distance Between Two Parallel Lines, Side, Metric Relations. 

Geometry Problem 787
Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations. 

Geometry Problem 786
Right Triangle, Altitude, Hypotenuse, Cevian, Perpendicular, Ratio, Metric relations. 

Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations. 

Geometry Problem
700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of
a side, Metric Relations. 

Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations. 

Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations. 

Geometry Problem 651.
Archimedes Book of Lemmas: Proposition 11
Perpendicular chords, Arcs, Radius. 

Geometry Problem 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular. 

Geometry Problem
608
Square with Right Triangles, Metric Relations, Congruence, Measurement. 

Geometry Problem
607
Intersecting Circles, Triangles, Metric Relations, Measurement. 

Geometry Problem
605
Post a comment or solution
Circle, Square, Chord, Perpendicular, Circular Segment, Metric Relations. 

Problem
582.
Quadrilateral, Diagonals, Incenters, Metric Relations. 

Problem
571.
Circle, Diameter, Chord, Perpendicular, Measurement. 

Problem
544.
Right Triangle, Altitude, Median, Equal angles, Measure. 

Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Chord, Perpendicular, Congruence. 

Problem
534.
Right Triangle, Squares, Perpendicular, Dissection, Areas. 

Problem
528.
Triangle, Medians, Perpendicular, Measurement. 

Problem 522.
Right Triangle, Circle, Diameter, Tangent. 

Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius. 

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement. 

Proposed Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement. 

Proposed Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement. 

Proposed
Problem 459.
Right triangle, Squares, Distance, Measurement. 

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent,
Measurement. 

Proposed Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord. 

Proposed
Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement. 

Proposed
Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement. 

Proposed
Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.
Pythagoras 

Proposed
Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence. 

Proposed
Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity. 

Proposed
Problem 336.
Two equal circles, a Common Tangent and a Square. 

Proposed Problem
317.
Right triangle and Inscribed Squares. 

Proposed Problem 316.
Circular segments and Inscribed Squares. 

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

Proposed Problem
303.
Triangle, Angle bisector of 90 degrees. 

Proposed Problem 284.
Circular Sector 90 degrees, Semicircles, Tangent, Radius. 

Proposed Problem 278.
Tangent Circles, Common External Tangent, Chord. 

Proposed Problem 277.
Tangent Circles, Common External Tangent. 

Proposed
Problem 276.
Square, 90 degree Arcs, Circle, Radius. 

Proposed Problem
275.
Right Triangle, Circumcircle, Sagitta, Inradius. 

Proposed Problem 271.
Tangent Circles, the Cube of the Common external tangent. 

Proposed Problem 270.
Tangent Circles, Common external tangent, Fractional exponents. 

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

Proposed Problem 268.
Right Triangle, Catheti and Altitude. 

Proposed
Problem 267.
Right Triangle, Product of Catheti. 

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

Proposed Problem 265.
Right Triangle, Pythagorean Theorem. 

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

Proposed Problem
239. Square, Midpoints, Lines, Congruence, Pythagoras.


Proposed Problem
207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse. 

Proposed Problem
204. Right Triangle, Incircle, Excircles, Inradius, Exradii. 

Proposed Problem
203. Right Triangle, Excircles, Exradii, Hypotenuse. 

Proposed Problem
202. Right Triangle, Incirle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter. 

Proposed Problem
201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter. 

Proposed Problem
200. Right Triangle, Incircle, Excircles, Points of Tangency, Inradius. 

Proposed Problem 190. Tangent
circles, Tangent chord, Perpendicular, Distance, Intersection of a Line
with a Circle, Diameter. 

Proposed Problem
183. Right Triangle, Hypotenuse Trisection Points, Squares of the Distances. 






