Maximum Altitude?

Geometry Level pending

Triangle A B C ABC has altitudes A D , \overline{AD}, B E , \overline{BE}, and C F . \overline{CF}. If A D = 12 , AD = 12, B E = 14 , BE = 14, and C F CF is a positive integer, then find the largest possible value of C F . CF.


The answer is 83.

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