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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.

 May 1, 2020
 #1
avatar+657 
0

ignore this ....

 May 1, 2020
edited by LuckyDucky  May 1, 2020
 #2
avatar+657 
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Is that correct?

LuckyDucky  May 1, 2020
 #3
avatar+111329 
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This is a rather difficult problem solved here by one of our best mathematicians, heureka

 

https://web2.0calc.com/questions/geometry_136

 

[ i'd like to go through this one myself   !!!  ]

 

cool cool cool

 May 1, 2020
 #4
avatar+657 
+2

oops

LuckyDucky  May 1, 2020
 #5
avatar+111329 
+1

Don't worry, LuckyDucky.....this problem would give a lot of people trouble  !!!

 

cool cool cool

CPhill  May 1, 2020

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