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 $4$ $4$ . If side AC has a length of $18$ $18$ , what is the length of side BC?

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Answer 1 · 2016-06-17T17:21:52

$B C = 10 .$ $BC=10.$

Let the angle-bisector of $∠ A$ $/_A$ meet BC in pt. $D .$ $D.$

then, by the property of angle-bisector, we have $(BD)/(DC)=(AB)/(AC)............(1)$

But, given that, $BD=4,AB=12, AC=18.$

$:.$ by $(1),$ 4/(DC)=12/18=4/6.#

Evidently, $DC=6,$ giving, $BC=BD+DC=4+6=10.$

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 4 44 . If side AC has a length of 18 1818 , what is the length of side BC?