Proposition: Given four concyclic points (lie on
the same circumference) A,B,C,D, if four circles through AB,
BC, CD, and AD are drawn, prove that the remaining four intersections points
A', B', C', and D' of successive circles are concyclic.

Apollonius for iPad: Four Circles Theorem, Problem 756
I drew the geometric construction above using Apollonius for iPad.
Apollonius is an interactive geometry app (IGS, or Dynamic Geometry
Environment, DGE). It allows you to create geometric constructions, such as those that can be made using a ruler and a compass, and subsequently move parts of your constructions to explore the relationship between the geometric objects on the screen.
Apollonius is inspired by software such as GeoGebra, The Geometer's Sketchpad and Cabri,
but its interface is especially designed for touch screen.
Download on the App Store:
Apollonius for iPad  Adolfo Rodriguez.
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741750

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Common Chord

Cyclic Quadrilateral

Four Circles Theorem 
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