Question

In a ΔABC, AD is the bisector of ∠A, meeting side BC at D.

If AD = 5.6 cm, BC = 6cm and BD = 3.2 cm, find AC.

Answer 1

We have,

In ΔABC, AD is the bisector of ∠A.

We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the containing the angle.

`therefore"AB"/"AC"="BD"/"DC"`

⇒ `5.6/"AC"=3.2/(6-3.2)`     [∵ DC = BC – BD]

⇒ `5.6/"AC"=3.2/2.8`

⇒ `"AC"=(5.6xx2.8)/3.2`

= `(5.6xx7)/8=0.7xx7`

= 4.9 cm