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Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

In ABC if ...

Question

In $△ A B C$ if $A D$ of is bisector of $∠ A$ and $A B = 8 c m, B D = 5 c m$ and $D C = 4 c m$ , then find $A C$

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Solution

In $△ A B C$
$A D$ , bisect vertex angle $A$
$∠ B A D = ∠ C A D$
$\frac{A B}{A C} = \frac{B D}{D C}$
$\Rightarrow$ $\frac{8}{A C} = \frac{5}{4}$
$\Rightarrow$ $5 A C = 8 \times 4$
$\Rightarrow$ $A C = \frac{32}{5} = 6.4 c m$

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Similar questions

In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

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In fig, $A D$ is the angle bisector of $∠ A$ . If $B D = 4 c m, D C = 3 c m$ and $A B = 6 c m$ , determine $A C$ .

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△ A B C, ∠ A B C = ∠ D A C, A B = 8 c m, A C = 4 c m, A D = 5 c m

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C D

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