In △ABC, D is a point on BC such that AD is the bisector of ∠A, AB = 11.7 cm, AC = 7.8 cm and BC = 13 cm. What is the length (in cm) of DC?

5.2

Ad is bisector of angle A ,

\(\frac{AB}{AC}\) = \(\frac{BD}{DC}\)

\(\frac{11.7}{7.8}\) = \(\frac{BD}{DC}\)

\(\frac{3}{2}\) = \(\frac{BD}{DC}\)

Ratio of BD and DC = 3 : 2

According to question ,

( 3 + 2 )R = 13

5R = 13

1R = \(\frac{13}{5}\) 

Now, DC = 2R = 2 × \(\frac{13}{5}\) 

= \(\frac{26}{5}\) 

= 5.2 cm