Multiple choice

In ∆ABC internal angle bisector of ∠A meets BC at D. If AB = 15 cm, AC = 13 cm and BC = 14 cm, then find the value of DC ?

  1. 6.5 cm

  2. 8 cm

  3. 7.5 cm

  4. 8.5 cm
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A Correct answer
Explanation

Use the Angle Bisector Theorem, which states that the angle bisector divides the opposite side proportionally to the adjacent sides: BD/DC = AB/AC = 15/13. Since BC = 14 cm, we have BD + DC = 14. From the ratio, BD = (15/28) × 14 = 7.5 cm, and DC = (13/28) × 14 = 6.5 cm.

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