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A triangle has corners 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 #4 #. If side AC has a length of #10 #, what is the length of side BC?

Answer 1

#BC=7.333#

According to angle bisector theorem, in a #DeltaABC#, if angle #A# is bisected and it cuts #BC# at #D#, then

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

As #AB=12#, #AC=10# and distance between the intersection of point A's angle bisector with side BC and point B i.e. #BD# is #4#,

we have #12/10=4/(DC)#

or #DC=(10xx4)/12=(10xxcancel4)/(3cancel12)=10/3=3.333#

Hence #BC=4+3.333=7.333#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.