Apollonius Revisited Equidistance

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CCCTask: Construct a circle through tangent to three circles A,B,CSolution: via intersection of two hyperbolasKey Observation: The center of the tangent circle is equidistant to three circles. Equilocusof two circles is a hyperbola.Exercise: There are actually 8 possible solutions to this problem (Why? Hint: 2*2*2=8)Some of these solutions involve the tangent circle containing some or all of the givencircles on the inside. Explore these possibilities. You may wish to review ellipse as anequilocus.
Challenge: Study special cases not covered above such as a circle being inside anotherone in the CCP case etc.Challenge: Using all the techniques described here construct several levels of inscribedtangent circles in a triangle.Challenge: Using all the techniques described here construct several levels of theApollonian Gasket.
Page 1 and 2: Apollonius Revisited:EquidistanceA
Page 3 and 4: Introduction and Motivation:Apollon
Page 5 and 6: Distance between: A circle C and a
Page 7 and 8: (B) EQUIDISTANCEDefinition: A point
Page 9 and 10: Research: Construct and investigate
Page 11 and 12: Equilocus of:(a)Two intersecting li
Page 13 and 14: Equilocus of: A circle C and a poin
Page 15 and 16: Equilocus of: Two external circles
Page 17 and 18: Equilocus of: Two circles D inside
Page 19 and 20: (D) Apollonius Tangency Problems: E
Page 21 and 22: LLLTask: Construct a circle tangent
Page 23 and 24: LLCTask: Construct a circle tangent
Page 25: CCLTask: Construct a circle tangent
Page 29 and 30: (c) a point and a hyperbolaAdvanced
Page 31 and 32: - Construct the perpendicular bisec
Page 33 and 34: -Hide all but the Focus, the direct
Page 35 and 36: -Construct a segment between M and
Page 37 and 38: - This tool will be handy if, say,
Page 39 and 40: Note: The difference between the di
Page 41 and 42: -Create a movable free point M on t
Page 43 and 44: -Hide all but the loci and two poin
Page 45 and 46: -Construct E and F, the intersectio

Apollonius Revisited Equidistance

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