### Two Intersecting Circles: What is this about?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2018 Alexander BogomolnyThe applet illustrates a problem suggested by Bui Quang Tuan:

Let two circles C(P) and C(Q) intersect in points C and D. A line through C intersects the second time C(P) at A and C(Q) at B. Let O be the midpoint of PQ. Then the circle C(O) with center O through C and D meets AB at the midpoint T. |

What if applet does not run? |

The fact is practically algebraic.

Let X, Y, Z be the midpoints of AB, AC, and BC, respectively. Introduce

For T to be the midpoint of AB we should have

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Copyright © 1996-2018 Alexander Bogomolny