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  • The Use of Inversion in Classical Geometry
  • Circle Inversion
  • Ptolemy's Theorem
  • Nine-Point Circle
  • Apollonius' Problem
  • Peaucellier linkage

The Use of Inversion in Classical Geometry

Author:
Christine Liu
Topic:
Circle, Geometry
The Use of Inversion in Classical Geometry
The Use of Inversion in Classical Geometry

Table of Contents

  • Circle Inversion

    • Definition of circle inversion
    • ΔOAB ~ ΔOB’A’
    • Different cases for circle inversion of circles and lines
    • Objects that are tangent to each other, are inverted to objects that are also tangent to each other.
    • If a circle d is inverted in another circle c, then d is inverted to itself if and only if c and d are perpendicular.
  • Ptolemy's Theorem

    • Definition of Ptolemy's Theorem
    • Proof using circle inversion
  • Nine-Point Circle

    • In any triangle, the mid-points of the sides, the feet of altitudes, and the mid-points of the segments that join the orthocentre H with each vertex all lie on a common circle.
    • The centre of the nine-point circle lies on the Euler line and is the mid-point of the circumcentre O and the orthocentre H.
    • Feuerbach's Theorem
    • Feuerbach's Theorem proof using circle inversion
    • Nine-Point Conic
    • Generalization of Euler Line
    • Lester's Theorem
  • Apollonius' Problem

    • CCC with Illustration
    • LLC
    • PPC
    • PCC
    • Apollonian Gasket
    • Soddy Circles
    • Ford Circles
    • PPP
    • LLL
    • PPL
    • PLL
    • PLC
    • LCC
    • CCC
  • Peaucellier linkage

    • Peaucellier Linkage
Next
Definition of circle inversion

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