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In triangle ABC, AB = 6 cm, AC = 3 cm and ∠BAC = 120°. The bisector of ∠A meets BC at D. How long is AD?

Competition practiceGeometry

A2 cm
B3 cm
C4.5 cm
D1.5 cm

Step-by-Step Solution

Area ABD + area ADC = area ABC. With AD =

d

and each half-angle 60°:

\frac{1}{2} (6) d sin 60° + \frac{1}{2} (3) d sin 60° = \frac{1}{2} (6) (3) sin 120°

, so

9 d = 18

and

d = 2

cm.

Answer: A) 2 cm

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