In a ΔABC, AD is the bisector of ∠BAC If AB = 6 cm, AC = 5 cm and

1.	In a ΔABC, AD is the bisector of ∠BAC If AB = 6 cm, AC = 5 cm and BD = 3 cm„ then DC =A. 11.3 cm B. 2.5 cm C. 3 5 cm D. None of these.
Answer» Given AD is the bisector of ∠BAC. AB = 6 cm, AC = 5 cm and BD = 3 cm. We know that the internal bisector of angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle. ⇒ \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\) ⇒ \(\frac{6}{5}\) = \(\frac{3}{DC}\) ∴ DC = 2.5 cm

In a ΔABC, AD is the bisector of ∠BAC If AB = 6 cm, AC = 5 cm and BD = 3 cm„ then DC =A. 11.3 cm B. 2.5 cm C. 3 5 cm D. None of these.

Answer»

Given AD is the bisector of ∠BAC. AB = 6 cm, AC = 5 cm and BD = 3 cm.

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

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

⇒ \(\frac{6}{5}\) = \(\frac{3}{DC}\)

∴ DC = 2.5 cm