The bisector of ∠B in ΔABC meets AC at D. If AB = 10 cm, BC = 11 cm and AC = 14 cm, then the length of AD is∶
20/3 cm
By the Angle Bisector Theorem, the bisector of \(\angle B\) divides the opposite side AC in the ratio of the adjacent sides:
\[\frac{AD}{DC} = \frac{AB}{BC} = \frac{10}{11}\]
Let \(AD = 10k\) and \(DC = 11k\). Since \(AD + DC = AC = 14\):
\[21k = 14 \implies k = \tfrac{2}{3}\]
Therefore \(AD = 10k = \dfrac{20}{3}\) cm.
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