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?
Answer & explanation
Correct answer: option 1
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