Multiple choice

In △ABC,AB=7" " cm,BC=12" " cm and AC=9" " cm. If AD is the angle bisector of ∠BAC, where D is a point on BC then BD is equal to:

  1. 5.5 cm

  2. 5.25cm

  3. 4.75cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By the Angle Bisector Theorem: BD/DC = AB/AC = 7/9. Since BD + DC = BC = 12 cm, we have BD = (7/16) × 12 = 84/16 = 5.25 cm. This follows directly from the theorem which states that an angle bisector divides the opposite side proportionally to the adjacent sides. Option B is correct.

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