You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

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

In ABC, the...

Question

In $△$ ABC, the bisector of $∠$ A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

Open in App

Solution

Given $A B = 18$ cm, $A C = 15$ cm and $B C = 22$ cm

By angle bisector theorem, if bisector of $∠ A$ meets side $B C$ at $D$ , then

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

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

Substituting values of $A B, A C$ and $B C$

$\frac{18}{15} = \frac{B D}{22 - B D}$

$\frac{6}{5} = \frac{B D}{22 - B D}$

$(22 * 6) - 6 B D = 5 B D$

$∴ B D = 12$ cm.

Suggest Corrections

Similar questions

Q. In ∆ABC, the bisector of ∠A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

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