While playing around on Geogebra, I found a curious theorem:
For all triangles \(\triangle ABC\), draw the circles with diameter as each of its sides. Call the circle passing through points \(A\) and \(B\) circle \(O_C\), and ditto for the other two circles. This theorem states that circles \(O_A\), \(O_B\), and line \(AB\) are concurrent, and ditto for the other two cases.
Your challenge: prove this theorem! Also, what is the significance of the concurrency points \(X,Y,Z\)? Is there a simpler way to define these points?
If this is actually a real theorem, please point me to the name of it.