The dynamic geometry figure below shows four green circles c_{1}, c_{2}, c_{3}, and
c_{4} passing through a point P. Circles c_{1} and c_{2} intersect at P_{12}, and so
on, P_{13}, P_{23}, P_{24}, P_{14}, and P_{34}. Red Circle c_{123} passes through P_{12}, P_{23},
and P_{13}, and so on. Prove that the four red circles pass
through a point M.

Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

- To explore (show / hide): click/tap a check box.
- To stop/play the animation: click/tap the icon in the lower left corner.
- To go to first step: click/tap the "Go to step 1" button.
- To manipulate the interactive figure: click/tap and drag the blue points or figures.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.

Geometry Problems

Open Problems

Visual Index

Ten problems: 1411-1420

All Problems

Circle

Intersecting Circles

Classical Theorems

GeoGebra

HTML5 and Dynamic Geometry

iPad Apps

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