I need help with altitudes
Triangle ABC has altitudes AD, BE, and CF. If AD = 12, BE = 12, and CF is a positive integer, then find the largest possible value of CF.
1/12 + 1/12 > 1/CF, solve for CF
CF > 6
Which means the minimum of 3rd altitude ==7.
Because the two given altitudes are 12 and 12, that means the triangle is an isosceles triangle. When the 2 altitudes are the same, the 3rd altitude has no " largest possible value", as long as the 3rd angle can be measured.