In $△ A B C$ , $A D$ is the bisector of $∠ A$ . If $B C = 10 c m$ , $B D = 6 c m$ and $A C = 6 c m$ , find $A B$ .

9 c m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $9 c m$
Given, AD bisects $∠ A$

Thus, by Angle Bisector Theorem,
$\frac{A B}{A C} = \frac{B D}{D C}$
$\frac{A B}{A C} = \frac{B D}{B C - B D}$
$\frac{A B}{6} = \frac{6}{10 - 6}$
$A B = \frac{6 \times 6}{4}$
$A B = 9$ cm

Suggest Corrections

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.

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