# 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 Pythagorean Curiosity Triangles and squares, fifteen conclusions.

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.

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

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
Circle, Square, Chord, Perpendicular, Circular Segment, Metric Relations.

Problem 582.

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.

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 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.

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