Question
In triangle ABC, AB = 8 cm, AC = 6 cm and BC = 10 cm.
The bisector of angle A meets side BC at point D. What is the length of BD (in cm)?Solution
ATQ, By internal angle bisector theorem: BD / DC = AB / AC = 8 / 6 = 4 / 3. Let BD = 4k, DC = 3k. Then BC = BD + DC = 4k + 3k = 7k = 10 ⇒ k = 10/7. So BD = 4k = 4 × 10/7 = 40/7 cm.
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