Can someone help me with this question?
Triangle ABC has altitudes AD, BE, and CF. If AD = 12, BE = 14, and CF is a positive integer, then find the largest possible value of CF.
I've drawn a diagram and tried considering the area and triangle inequalities, but I don't know what to do next.
This is a rather difficult problem solved here by one of our best mathematicians, heureka
[ i'd like to go through this one myself !!! ]