Given an not Equilateral Triangle with following side sizes: 45,60,75. Find a sum of distances from a random located point inside a triangle to its three sides.
Note 1: Viviani's theorem related only to equilateral triangles.
Note 2: Fermat point is related to the minimization of distances from a random point inside the triangle and its vertices.
As we can see that both notes are not helpful to solve that problem.
I have been given that puzzle during an hour an a half exam. There were only 6 minutes to solve that problem. Afters many hours I still do not have an answer. I will be very glad to get some assistance or maybe the whole solution
Regards, Dany B.