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Standard IX

Mathematics

Trigonometric Ratio(sin,cos,tan)

If AD is bise...

Question

If AD is bisector of interior $∠$ A of a triangle ABC and $A B = 10 c m, A C = 6 c m, B D = 12 c m$ , then $C D =$ ?

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Solution

The correct option is B $7.2$ cm
We have,

$\frac{A B}{A C} = \frac{B D}{D C} \Rightarrow \frac{10}{6} = \frac{12}{C D}$

$\Rightarrow C D = \frac{12 \times 6}{10} = 7.2 c m$

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Similar questions

Q. In given figure, check whether AD is the bisector of

∠

A of

△

ABC in each of the following:

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm

(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm

(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm

(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm

(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

In a triangle ABC, AD is the angular bisector and BD: DC = 2:1. If AB = 12 cm, find AC.

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 Fig 7.59, check whether AD is the bisector of $∠ A$ of $Δ A B C$ in each of the following:
(i) AB =5 cm,AC= 10cm, BD= 1.5 cm and CD=3.5ccm
(ii) AB = 4 cm. AC = 6 cm, BD =1.6cm and CD = 2.4 cm
(iii) AB =8 cm, AC=24 cm, BD=6cm and BC = 24cm
(iv) AB=6cm,AC=8 cm, BD=1.5 cm and CD = 2cm
(v) AB= 5 cm, AC= 12cm, BD = 2.5cm and BC = 9 cm

Q. In a ∆ABC, AD is the bisector of ∠BAC. If AB = 8 cm, BD = 6 cm and DC = 3 cm. Find AC

(a) 4 cm
(b) 6 cm
(c) 3 cm
(d) 8 cm

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If AD is bisector of interior ∠ A of a triangle ABC and AB=10cm,AC=6cm,BD=12cm, then CD= ?

The correct option is B 7.2 cmWe have,ABAC=BDDC⇒106=12CD⇒CD=12×610=7.2 cm

If AD is bisector of interior $∠$ A of a triangle ABC and $A B = 10 c m, A C = 6 c m, B D = 12 c m$ , then $C D =$ ?

The correct option is B $7.2$ cm
We have,

$\frac{A B}{A C} = \frac{B D}{D C} \Rightarrow \frac{10}{6} = \frac{12}{C D}$

$\Rightarrow C D = \frac{12 \times 6}{10} = 7.2 c m$