A triangle has corners at points A, B, and C. Side AB has a length of $12$ . The distance between the intersection of point A's angle bisector with side BC and point B is $9$ . If side AC has a length of $16$ , what is the length of side BC?

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Answer 1 · 2017-12-21T09:36:26

Length of side BC = 21

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

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

$(AB)/(AC)=(BD)/(DC)$

$12 / 16 = 9 / (DC)$

$DC = (9*16) / 12 = 12$

$BC = BD+DC= 9+12 =21$

A triangle has corners at points A, B, and C. Side AB has a length of 12 12 . The distance between the intersection of point A's angle bisector with side BC and point B is 9 9 . If side AC has a length of 16 16 , what is the length of side BC?