Online Geometry

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

Metric Relations in a Right Triangle

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.

Pythagoras_extension

The General Extension to Pythagoras' Theorem.

Pythagoras curiosity. Online tutoring.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.

Einstein and Pythagoras theorem proof
 

iPad Geoboard: Pythagorean Theorem proof by Leonardo 

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

de Gua's theorem

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

iPad Geoboard: Pythagorean Theorem proof 

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

Pythagorean spiral or Square Root Spiral or Spiral of Theodorus

Pythagorean spiral or Square Root Spiral or Spiral of Theodorus.

Geometry Problem 1022

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

Geometry Problem 1013

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

Geometry Problem 973

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

Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations

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

Right Triangle, Altitude, Hypotenuse, Cevian, Perpendicular, Ratio

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

Isosceles Triangle, Circle, Diameter, Altitude, Chord

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

Equilateral triangle, Circle

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

Equilateral triangle, Circle

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

Circles, Diameter, Tangent, Metric Relations

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

Archimedes Book of Lemmas Proposition 11

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

Tangent Circles

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

Square with Right triangles

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

Intersecting Circles

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

Square, Circle, Metric Relation

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

Quadrilateral, Diagonals, Incenters

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

Online Math: Geometry Problem 571, Circle

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

Right Triangle, Altitude, Median, Equal angles, Measure

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

Cyclic quadrilateral, Diagonal, Diameter

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

Right triangle, square, area

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

Triangle, Medians, Perpendicular

Problem 528.
Triangle, Medians, Perpendicular, Measurement.

Geometry Problem: Right triangle, Circle, Tangent

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

Elearn 491: Square, Incircles, Radius, Side

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

Square, Circles, Tangent

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

Three tangent circles, Radius, Distance

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

Circle, Tangent, Perpendicular, Radius

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

Right triangle, Squares

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

Square, Circle, Tangent

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

Circle, Diameter, Sagitta

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

Tangent Circles, Chords, Perpendiculars

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

Tangent Circles, Chords, Perpendiculars

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

Regular pentagon

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

RIght triangle, Midpoints, Distance

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

Square, 45 degrees

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

Tangent circles, Square

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

Elearning 317 Right triangle

Proposed Problem 317.
Right triangle and Inscribed Squares.

Circular Segments, Inscribed Squares

Proposed Problem 316.
Circular segments and Inscribed Squares.

Tangent circles and line

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

Triangle and angle bisector of 90 degrees

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

Elearning 284: Circular Sector

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

Tangent Circles, Common External Tangent, Chord

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

Tangent Circles

Proposed Problem 277.
Tangent Circles, Common External Tangent.

Square, Circle, 90 Arc

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

Sagitta Problem

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

Cube of the external common tangent

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

Tangent circles, common tangent 

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

Right triangle, Altitude, perpendiculars

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

Right triangle, Altitude, Catheti

Proposed Problem 268.
Right Triangle, Catheti and Altitude.

Right triangle, Catheti product

Proposed Problem 267.
Right Triangle, Product of Catheti.

Right triangle, Altitude, Geometric Mean

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

Pythagorean Theorem

Proposed Problem 265.
Right Triangle, Pythagorean Theorem.

Right triangle

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

Square, Midpoint, Congruence, Pythagoras

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

Problem 207: Hypotenuse

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

Elearn 204

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

Problem 203

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

Problem 202 Right triangle, excircles

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

Elearn 201

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

Elearning 200: Right Triangle

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

Elearning 190 tangent circles, chord, perpendicular

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

Right triangle, Hypotenuse trisection

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

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