Question 116
In a triangle ABC, AD is the bisector of angle A If AC = 4.2 cm , DC = 6 cm, BC =10 cm , then find AB ?
Solution
We can use the Angle Bisector Theorem:
In triangle ABC, if AD bisects ∠A, then $$\dfrac{AB}{AC}=\dfrac{BD}{DC}$$
We know: BC=10 and DC=6
So, BD = BC − DC = 10 − 6 = 4
Applying the theorem
$$\dfrac{AB}{AC}=\dfrac{BD}{DC}$$
Given
AC=4.2, so:$$AB=\dfrac{2}{3}\times4.2=2.8\ cm$$
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