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If AD is the internal angle bisector of \( \Large \triangle ABC \) with AB = 3 cm and AC = 1 cm, then what is BD : BC equal to?

A) 1: 3
B) 1: 4
C) 2 : 3
D) 3: 4

Correct Answer:




D) 3: 4

Description for Correct answer:

\( \Large \triangle ABC, AD is\ the\ internal\ angle\ bisector\ of\ \angle A.\\ Using\ property\ of\ internal\ angle\ bisector. \)

\( \Large \frac{BD}{CD} = \frac{AB}{AC} \)

=> \( \Large \frac{CD}{BD} = \frac{AC}{AB} \)

=> \( \Large \frac{CD}{BD}+1 = \frac{AC}{AB}+1 \)

=> \( \Large \frac{CD + BD}{BD} = \frac{AC + AB}{AB} \)

=> \( \Large \frac{BC}{BD} = \frac{3+1}{3} => \frac{BD}{BC} = \frac{3}{4} \)

\( \Large \therefore BD : BC = 3 : 4 \)

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

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