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

Let ABC be a triangle. Let A' be the contact point of the excircle opposite A with BC. Let A'' be the reflection of A' in the line through the contact points of 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.