Dear Alex,

Thank you for putting my name in the theorem! This interesting fact based on very well-known geometrical essence and I only have found another configuration from another view point for it. I do not sure that it is new one. If any one known another reference before, please give us so we can have full history!

Dear Alex, please correct in your explaining text:
"Next inscribe circle C1 into <A1A2A3 so that it is to A1A2 at T12"
I think it must be:
"Next inscribe circle C2 into <A1A2A3 so that it is tangent to A1A2 at T12"

Please put also all names: A1, A2, A3, C1, C2, C3, C4, C5, C6, T12, T23,... in the applet so we can use in the future!

Best regards,
Bui Quang Tuan