Question

in ∆ ABC, ray BC is bisect angle ABC if AD=6, DC =8, AB=9 find BC. ​

Answer 1

By Angle bisector theorem: which states that, the ratio of any 2 sides of a triangle is equal to the ratio of the lengths of the segments formed on its third side, by the angle bisector of the angle formed by those 2 sides.

So, here, AB/BC = AD/DC

=> 9/BC = 6 / 8

=> BC = 8*9/6 = 8*3/2 = 4*3 = 12 cm

There is some mistake in question plz check n correct!

Answer 2

Given:-

ray BC is a bisector of angle ABC.

AD = 6, DC = 8, AB = 9

To Find:-

value of BC.

Solution:-

In ∆ ABC, ray BC is bisect angle ABC

•°• By Angle bisector theorem

•°• AB/BC = AD/DC

9/BC = 6/8

9/BC = 3/4

BC × 3 = 9 × 4

BC × 3 = 36

BC = 36/3

BC = 12

• Answer

Value for BC is 12.

More information:-

1)Basic proportionality theorem.

In triangle ABC, if seg PQ || seg AC then AP/BP = QC/BQ.

2) Converse of basic proportionality

theorem.

In triangle PQR, PS/SQ = PT/TR then seg ST || QR.

3) Theorem of bisector of an angle of

a triangle. If in triangle ABC, BD is bisector of triangle ABC, then AB/BC = AD/DC.

(4) Property of three parallel lines and

their transversals. If line AX || line BY || line CZ and line l and line m are their transversals then AB/BC = XY/YZ