In a ΔABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and

1.	In a ΔABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. Find ACA. 4 cm B. 6 cm C. 3 cm D. 8 cm
Answer» Given AD is the bisector of ∠BAC. AB = 8 cm, DC = 3 cm and BD = 6 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. ⇒ \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\) ⇒ \(\frac{8}{AC}\) = \(\frac{6}{3}\) ∴ AC = 4 cm

In a ΔABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. Find ACA. 4 cm B. 6 cm C. 3 cm D. 8 cm

Answer»

Given AD is the bisector of ∠BAC. AB = 8 cm, DC = 3 cm and BD = 6 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.

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

⇒ \(\frac{8}{AC}\) = \(\frac{6}{3}\)

∴ AC = 4 cm