Multiple choice

In △ABC,AB=8cm,BC=12 cm and AC=7cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then CD is equal to:

  1. 5.5cm

  2. 6cm

  3. 6.4cm

  4. 5.6cm

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the Angle Bisector Theorem: BD/DC = AB/AC = 8/7. Since BD + DC = BC = 12 cm, we can write DC = 12 * 7/(8+7) = 12 * 7/15 = 84/15 = 5.6 cm. The Angle Bisector Theorem states that the bisector of an angle divides the opposite side in the ratio of the adjacent sides.