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Let ABC be a triangle with orthocenter H. Let

be the point of tangency of CA with the excircle opposite A, and similarly define

, and

. Let

, and

. Let

, and

. Then AA', BB', and CC' as well as AA'', BB'', and CC'' meet at H.

See the paper "Synthetic proof of Paul Yiu's excircles theorem" available on Darij Grinberg's home page.

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A Concurrency of Lines through Points of Tangency with Excircles