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

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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

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

Aug 3, 2022
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sorry, thats not correct.

waterlili  Aug 3, 2022
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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

Aug 3, 2022
edited by CPhill  Aug 3, 2022
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you mean 4?

waterlili  Aug 3, 2022
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Oops!!!...I was in a hurry  !!

Corrected  !!!

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

CPhill  Aug 3, 2022
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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  !!!

Aug 3, 2022
edited by CPhill  Aug 3, 2022
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Thank you!!!!

waterlili  Aug 3, 2022
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No prob !!!

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

CPhill  Aug 3, 2022