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avatar+177 

 In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BC.

Related question:

 In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BZ.

 Aug 3, 2022
 #1
avatar
+1

By the angle bisector theorem, BC = 13/3.

 Aug 3, 2022
 #2
avatar+177 
+4

sorry, thats not correct.

waterlili  Aug 3, 2022
 #3
avatar+124594 
+2

 In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BC.

 

Angle  Bisector Theorem

 

BC / CY = BA / AY

 

BC / 3 = 8 / 6

 

BC  =  3 * 8 /  6  =    24 / 6   =   4

 

 

cool cool cool

 Aug 3, 2022
edited by CPhill  Aug 3, 2022
 #5
avatar+177 
+4

you mean 4?

waterlili  Aug 3, 2022
 #6
avatar+124594 
+1

Oops!!!...I was in a hurry  !!

Corrected  !!!

 

This changes the answer to the other problem, too....will  correct  !!!

 

cool cool cool

CPhill  Aug 3, 2022
 #4
avatar+124594 
+2

 In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BZ.

 

In the other problem we found that BC = 4

 

So, again, by the angle bisector theorem

 

AC / BC = AZ / BZ

 

9 / 4  =  AZ / BZ

 

So....there  are 13 parts to AB

 

And BZ  =  4 of them

 

So

BZ =  (4/13)(AB)  =  (4/13)(8) =   32/ 13

 

CORRECTED  !!!

 

cool cool cool

 Aug 3, 2022
edited by CPhill  Aug 3, 2022
 #7
avatar+177 
+5

Thank you!!!!

waterlili  Aug 3, 2022
 #8
avatar+124594 
+1

No prob !!!

 

{Well, I guess there were a couple of them....LOL!!! }

 

cool cool cool

CPhill  Aug 3, 2022

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