Question

In a triangle $ABC$, $AD$ is the bisector of angle $A$. If $AC = 4.2	ext{ cm}$, $DC = 6	ext{ cm}$, $BC = 10	ext{ cm}$, find $AB$.

Accepted Answer

C. By Angle Bisector Theorem: $$\frac{BD}{DC} = \frac{AB}{AC}$$ Given $BC = 10	ext{ cm}, DC = 6	ext{ cm} \implies BD = 10 - 6 = 4	ext{ cm}$. $$\frac{4}{6} = \frac{AB}{4.2} \implies AB = \frac{4 	imes 4.2}{6} = 2.8	ext{ cm}$$

Angle bisector theorem

Explanation

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