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