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M is the midpoint of line AB and N is the midpoint of line AC, and T is the intersection of line BN and line CM. If line BN is perpendicular to line AC, BN=12, and AC=14, then find CT.

beastrohit  Nov 28, 2018
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Since  M is a median of AB and  N is the median of AC, their intersection occurs (2/3) of the way from vertex B to N

 

So... TN     is (1/3) of the distance from B to N =  (1/3)(12) = 4

 

And  TNC  is a right triangle  with legs NC, TN  and hypotenuse CT

 

So

 

CT  =  sqrt ( NC^2 + TN^2 )  =  sqrt ( 7^2 + 4^2) = sqrt ( 65)

 

 

cool cool cool

CPhill  Nov 28, 2018

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