A triangle has corners at points A, B, and C. Side AB has a length of $16$ $16$ . The distance between the intersection of point A's angle bisector with side BC and point B is $8$ $8$ . If side AC has a length of $27$ $27$ , what is the length of side BC?

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Answer 1 · 2017-12-21T09:42:37

Length of side BC = 21.5

Let the point where the angle bisector intersects with
side BC be D

$using the angle bisector theorem$ $"using the "color(blue)"angle bisector theorem"$

$\frac{A B}{A C} = \frac{B D}{D C}$ $(AB)/(AC)=(BD)/(DC)$

$\frac{16}{27} = \frac{8}{D C}$ $16 / 27 = 8 / (DC)$

$D C = \frac{8 \cdot 27}{16} = 13.5$ $DC = (8*27) / 16 = 13.5$

$B C = B D + D C = 8 + 13.5 = 21.5$ $BC = BD+DC= 8+13.5 =21.5$

A triangle has corners at points A, B, and C. Side AB has a length of 1616 . The distance between the intersection of point A's angle bisector with side BC and point B is 88 . If side AC has a length of 2727 , what is the length of side BC?