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In triangle ABC, let M be the midpoint of AB and N be on AC such that N is an altitude of ABC.  If AB = AC = 13 and BC = \(18\), and AN and CM intersect at X, then what is AX?

 

 Apr 24, 2022
 #1
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This triangle is  isoceles  so  AN  and  CM  are medians

 

ANB forms aright triangle  with  NB  = 9

 

AN = sqrt  [ 13^2  - 9^2 ]   = sqrt  [ 88]  =  2sqrt (22)

 

By the property of medians 

 

AX = (2/3) AN =   (2/3) * 2sqrt (22) =   (4/3)sqrt (22)

 

 

cool cool cool

 Apr 24, 2022

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