<img src="https://tex.z-dn.net/?f=%24%5Coverline%7BBY%7D%24" id="TexFormula1" title="$\overline{BY}$" alt="$\overline{BY}$" alig

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2 years ago

n="absmiddle" class="latex-formula"> and $\overline{CZ}$ are angle bisectors of triangle ABC that meet at I as shown below, with CY = 4, AY = 6, and AB = 8. Find BZ.

Mathematics

1 answer:

erica [24]2 years ago

6 0

Answer:

BZ = 64/23 = 2 18/23

Step-by-step explanation:

The angle bisectors divide the triangle into proportional parts, so we have ...

CB/CY = AB/AY

CB = CY(AB/AY) = 4(8/6) = 16/3 . . . . multiply by CY and evaluate

and ...

BZ/CB = AZ/AC

BZ = AZ(CB/AC) . . . . multiply by CB

But we have ...

AZ = 8 -BZ, so this becomes ...

BZ = (8 -BZ)(16/3)/(10)

BZ(1 +8/15) = 64/15 . . . . add the BZ term on the right to both sides

BZ = (64/15)(15/23) = 64/23 . . . . divide by the coefficient of BZ

BZ = 64/23 = 2 18/23

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