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Visual Index

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Various Forms of Poncelet's Porism

Circle-Triangle-Escribed Circle Circle-Triangle-Escribed Circle
Circle-Triangle-Inscribed Circle Ellipse-Triangle-Inscribed Circle-Triangle-Inscribed Circle
Circle-Triangle-Inscribed Circle-Triangle-Inscribed Ellipse Circle-Quadrilateral-Inscribed Circle
Circle-Quadrilateral-Escribed Circle Circle-Quadrilateral-Escribed Circle
Circle-Quadrilateral-Inscribed Ellipse Circle-Quadrilateral-Four Tangential Circles
Circle-Triangle-two Tangential Circles Circle-Traingle-Two Escribed Circles
Circle-Quadrilateral-Two Escribed Circles Circle-Hexagon-Circle in Poncare's Model
Circle-Triangle-Circle in Poncare's Model Circle-Star-Circle in Poncare's Model
Circle-Triangle-Circle in Lobachevskian Model Parabola-Triangle-Inscribed Circle
Circle-Quadrilateral-Escribed Parabola Circle-Quadrilateral-Escribed Parabola

Constructions with the Compass Alone

Locating the Midpoint Locating the Center of a Circle
Osculating Circle of the Nephroid Osculating Circle of the Deltoid
Osculating Circle of the Astroid Osculating Circle of the Cardioid
Ellipse Parabola
Lemniscate Hyperbola
Bowditch Curve Nephroid
Cardioid Deltoid
Astroid Ellipse Constructed with Eight Circles
Regular Pentagon @

Constructions with the Ruler Alone

Conic Midpoint of a Line Segment, Given a Parallel Line
Parallel through a Given Point, Given the Midpoint @

Double Generation

Astroid Cardioid
Nephroid Deltoid
Trochoid @


Dissection of a Disk Dissection of One Square Into Three Squares
Dudeney's Trick Decomposition of Acute Triangles into Similar Pieces


Linkage to Generate Ellipse Linkage to Generate Cardioid
Linkage to Generate Cardioid Peaucellier's Linkage
Peaucellier's Linkage Peaucellier's Linkage
Area and Direction Preserving Linkage Hart's Linkage
Hart's Linkage Kempe's Linkage
Rotating Tangential Disks Pear
Four Rotating Disks Cashew

Epicycloids and Hypocyloids-Basic Constructions

Goormaghtigh's Construction of Deltoid Astroid
Astroid Deltoid
Cardioid Nephroid

Epicycloids and Hypocyloids-Various Properties

Cardioid and Six Circles Nephroid and Six Circles
Formation of Nephroid Two Cardioids and One Nephroid
Astroid and 4-cusped Epicycloid Deltoid and 3-cusped Epicycloid
Starfish Deltoid Sliding in Nephroid
Nephroid Sliding outside Cardioid Cardioid Enveloped by Circles
Tooth Wheel Coupling Nephroid Sliding Outside Deltoid
Epicycloids and Hypocycloids Deltoid Circumscribing a Given Triangle
Orthogonal Tangents of Deltoid Deltoid Sliding on Orthogonal Lines
Rotating Nephroids Meeting Orthogonally Orthogonal Normals of Deltoid
Moving Orthogonal Cardioids A Theorem of Hildebrand
Even Smaller Area... Orthogonal Tangents and Normals of the Cardioid
Cardioid Sliding on Orthogonal Lines @

Curves as Envelope of Tangents

Lines Enveloping the Nephroid Conic Enveloped by Lines
Cardioid Deltoid
Nephroid Astroid
Deltoid @

Osculating Circle and Involuate

Deltoid Hyperbola
Conics Trochoid
Cardioid Ellipse
Involute of the Deltoid Cardioid-Evolute and Involute
3-Cusped Epicycloid-Evolute and Involute Evolute of Astroid
Involute of Circle Evolute and Involute of 3-cusped Epicycloid


Schroeter's Construction of Regular Pentagon Regular Pentagon
Regular Pentagon Inscribing a Square In a Regular
Pentagon Determined by the Midpoints of its Sides @

Steiner's Porism

Steiner's Porism Steiner's Porism
Steiner's Porism-Basic Case Steiner's Porism
Degenerate Case of Steiner's Porism Degenerate Case of Steiner's Porism


Parabola: Given Axis, Focus and One Point Parabola: Given Two Tangents and
Points of Contact
Parabola Determined by Four Tangents Parabola Tangent to a Triangle
Parabolas from Four Points A Theorem of Hildebrand

Radical Axes

Radical Axes-Property 1 Radical Axes-Property 2
Radical Axes-Property 3 Radical Axes-Property 4
Radical Axes-Property 5 @


Colinearity Colinearity
Colinearity Neuberg's Theorem
Square Dance Square Passing Through Four Given Collinear Points

Coaxal System

Coaxal System Coaxal System
Coaxal System Coaxal System
Coaxal System Apollonius Circles
Tangents at Collinear Points @

Invariant Properties

Invariant Invariant
Invariant Invariant
Invariant Invariant
Invariant An Invariant Sum
Invariant Sum of Distances Same Length
Identical Sums of Lengths Identical Sums of Lengths
Unused IMO Problem from Sweden "Another Problem from the Common Room"
A Problem of Ian McGee Same Area
Same Area Same Area, Why?
When Three Circles of the Same Size Meet at One Point... @


C-Transform Dual C-Transform
Pole of a Line with respect to a Triangle Polar Line of a Point with respect to a Triangle
Every Obtuse Triangle is Self-Polar with respect to a Unique Circle An Unlikely Symmetry
Isogonal Conjugates @


Arbelos Problem of Apollonius
Haruki's Cevian Theorem for Circles A Degenerate Case of Haruki's Cevian Theorem for Circles
Circle Orthogonal to Three Given Circles Four Circles Meeting at One Point
Three Circles Each Pair Meeting at Two Points... When Three Circles Meet at One Point...
Circle of Antisimititude Circle Common Tangent to a Circle and a Conic
Orthogonal Tangents Rectangle Tangent to Two Circles
Colinear Points Parallel
A Japanese Temple Geometry Problem A Problem of Stanley Rabinowitz
A Problem of Stanley Rabinowitz Inspiration from Japanese Temple Geometry
Common Tangent Circles Circles Enveloping the Lemniscate
Mori Effect @


Similar Triangles round a Triangle Regular Triangle Determined by Regular Triangles
Equilateral Triangle Traveling on Lines Isoceles
Van Schooten's Locus Problem Regular Triangle on Three Concentric Circles
Tangents Enclosing Congruent Triangles Rigid Motion
Morley's Triangle Concurrent
Concurrent @


Conics from Paper Folding Ellipse Tangent to Astroid
Chords Parallel to a Diameter A Property of Conic
Circumscribing Rectangles of Conics Orthogonal Normals of a Conic
Six Rotating Ellipses Another Property of Conic
Octagon in Conic Given Four Points and One Tangent
Ellipse Tangent to Two Circles and their External Common Tangents Two Tangential Conics
Two Conics Three Tangential Conics
Three Conics Each Pair Meet at Four Points Conic Given by Five Tangents
Rectangular Hyperbola Poncelet's Construction
Four Mutually Tangential Ellipses Coaxal Conics
Ellipse and Its Tangent Conic Given by Two Tangents, Points of Contact and a Third Point
Ellipse  Inscribed in a Deltoid Deltoid Circumscribing to an Ellipse


Chebyshev Polynomials Chebyshev Polynomial
Bowditch Curve Cubic Interpolation Polynomial
Gerono Lemniscate Witch of Agnesi
Conchoid of Nicomedes Egg
Freeth's Nephroid Pearl


Quadrilateral in and Quadrilateral about a Cricle Centers of Gavity of Triangles
Every Quadrilateral May be Projected into a Parallelogram @

Seven Circles Theorem

Degenerate Case Seven Circles Theorem
Degenerate Case Degenerate Case
Degenerate Case Degenerate Case
Degenerate Case Degenerate Case


Equally Inclinded Tangents Find the Locus of Circumcenter
Envelope of Circles Equivalent Area
Design @