A triangle has corners 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 $6$ $6$ . If side AC has a length of $10$ $10$ , what is the length of side BC?

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Answer 1 · 2017-12-21T09:10:34

Length of BC = 11

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

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

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

$\frac{12}{10} = \frac{6}{D C}$ $12 / 10 = 6 / (DC)$

$DC = (cancel(6)*10) / (cancel(12)2) = 5$

$BC = BD+DC= 6+5 =11$

A triangle has corners points A, B, and C. Side AB has a length of 12 1212 . The distance between the intersection of point A's angle bisector with side BC and point B is 6 66 . If side AC has a length of 10 1010 , what is the length of side BC?