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Help Im bad at geometry

 

In triangle ABC, let the angle bisectors be BY and CZ. Given AB = 16, AY = 16, and CY = 16, find BC and BZ.

 Jun 27, 2023
 #1
avatar+274 
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https://web2.0calc.com/questions/angle-bisectors_27

 

I think you should use the angle bisector theorem and start from there.

 Jun 27, 2023
 #2
avatar+131 
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Let BC and BZ both equal x. The angle bisector theorem provides us with:

AC/AB = CZ/BZ

16/(16+x) = 16/y

We solve y in terms of x, and as a result,

y = 16(16+x)/16 = x+16

Upon substitution, we discover—

16/(16+x) = 16/(x+16)

If we cross-multiply, we obtain:

16(x+16) = 16(16+x)

Simplifying, we get:

16x + 256 = 256 + 16x

In light of the fact that 16x cancels on both sides, we are left with:

256 = 256

As a result, there exist an endless number of BC and BZ values that could satisfy the requirements.

 Jun 27, 2023

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