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I is the incenter of ABC.  Find DE.

 

 May 1, 2022
 #1
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Let C =  (0,0)   A =  (4,0)  and B = (0,3)

We have a 3-4-5 right triangle so BA =  5

 

We can find the coordinates of the incenter as  (  [ 4(3)  ] / 12  , [  3(4) / 12 ] =  (1 , 1)

 

Equation of line through   A and I   ....  y = (-1/3)(x - 4)

When x =  0    D = ( 0, 4/3)

 

Equation of line  through B and I  ......    y = (-2 / 1) x + 3

When y = 0,  E  =  (0, 3/2)

 

DE =   sqrt [ (4/3)^2  + (3/2)^2]   =   sqrt  [ 16/9 + 9/4 ]  =  sqrt  [  145 ] / 6   

 

 

cool cool cool

 May 1, 2022

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