In fig- A D is the bisector of - A - If B D-4 C M- D C-3 C M and A B-6 C M- Determine A C-

In ΔABC,AD is the bisector of ∠A ∴ ED/DC = AB/AC ⇒ 4/3 = 6/AC ⇒ 4AC = 18 ⇒ AC = 9/2 cm =4.5 cm ...

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Standard X

Mathematics

Internal Angle Bisector Theorem

In fig, A D i...

Question

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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Solution

In $Δ A B C$ , $A D$ is the bisector of $∠ A$
By Angle Bisector Theorem,

$\Rightarrow \frac{B D}{D C}$ = $\frac{A B}{A C}$

$\Rightarrow \frac{4}{3}$ = $\frac{6}{A C}$

$\Rightarrow 4 A C = 18$

$\Rightarrow A C = \frac{9}{2} c m = 4.5 c m$

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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.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

Q. In a

∆ A B C, A D

is the bisector or

∠ 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.
(iii) If AB = 5.6 cm, BD = 3.8 cm and BC = 6 cm, find AC.
(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

Q. In the figure given below

A D

is bisector of

∠ B A C

. If

A B = 6 c m, A C = 4 c m

and

B D = 3 c m

, find

B C

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

In $△ A B C, A B = 3 c m, A C = 4 c m$ and AD is the bisector of $∠$ A. Then, $B D = D C .$

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In fig, AD is the angle bisector of ∠A. If BD=4cm,DC=3cm and AB=6cm, determine AC.

In ΔABC, AD is the bisector of ∠ABy Angle Bisector Theorem, ⇒BDDC = ABAC ⇒43 = 6AC ⇒4AC=18 ⇒AC=92cm=4.5cm

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 $A C$ .

In $Δ A B C$ , $A D$ is the bisector of $∠ A$
By Angle Bisector Theorem,

$\Rightarrow \frac{B D}{D C}$ = $\frac{A B}{A C}$

$\Rightarrow \frac{4}{3}$ = $\frac{6}{A C}$

$\Rightarrow 4 A C = 18$

$\Rightarrow A C = \frac{9}{2} c m = 4.5 c m$