Question

In triangle ABC,AB=10 cm, Angle A is bisected internally to intersect BC at D. BD=6cm,and DC=7.5.
What is the length of CA.

Answer 1

Given: In triangle ABC,AB=10 cm, Angle A is bisected internally to intersect BC at D. BD = 6 cm,and DC=7.5.

To find: The length of CA.

Solution:  Since in Δ ABC, AB = 10.0 cm, BD = 6.0 cm and DC = 7.5 cm

Also, AD is the angle bisector of ∠A.

Now, we shall apply the angle bisector theorem.

AB / AC = BD / DC

or,   AC = AB× DC / BD

or,   AC = (10.0× 7.5) / 6.0

or,   AC = 12.5 cm