Let ABC be a triangle with Incircle ( I ), and let ( I ) touch BC, CA, AB at A', B', C', respectively, and A'',
B'', C'' are the midpoints of the sides BC, CA, AB, respectively.
One of the distances A'A", B'B", C'C" is equal of the sum of the two others. ( C'C'' + A'A" = B'B'' )
Thanks in advance for your time and help.