The Five Circle Theorem.
Miquel's Five-Circle Theorem is among a sequence of wonderful theorems in plane geometry bearing his name. It states that
By starting from a pentagon in the plane, one can
construct a 5-star whose ertices are the intersections of the non-neighboring edges of the
pentagon. If five circles are drawn such that each circle circumscribes a riangular corner of
the star, then the neighboring circles intersect at five new points which are cocircular.
Note: You can drag free points (red points) to see the effect.
See Also:
1. The proof of this theorem with Full-Anlge Method.
2. The proof with Deductive Database Method. |