A Concurrency from the Reflections of the Contact Points with the Excircles

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Let ABC be a triangle. Let A' be the contact point of the excircle

α

opposite A with BC. Let A'' be the reflection of A' in the line through the contact points of

α

with the extensions of AC and AB. Similarly define B'' and C''. Then AA'', BB'', and CC'' are concurrent at a point S, called the Schiffler point.