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