Question

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.

Answer 1

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