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Standard X

Mathematics

Internal Angle Bisector Theorem

In a Δ ABC, A...

Question

In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.

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Solution

Since,
AD is the bisector of ∠A meeting side BC at D in Δ ABC
Hence, Δ ABD ~ Δ ACD

Now,
⇒ $\frac{A B}{A C} = \frac{B D}{C D}$

⇒ $\frac{5}{4.2} = \frac{2.5}{C D}$

⇒ $5 \times C D = 2.5 \times 4.2$

⇒ $C D = 2.1 c m$

$∴$ DC = 2.1 cm.

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Similar questions

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∠ A

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Q. In a

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ABC, AD is the bisector of

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(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.

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Q. In

△ A B C

, the internal bisector

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and

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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

Q. In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.

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In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.

Since, AD is the bisector of ∠A meeting side BC at D in Δ ABC Hence, Δ ABD ~ Δ ACD Now, ⇒ABAC=BDCD ⇒54.2=2.5CD ⇒5×CD=2.5×4.2 ⇒CD=2.1 cm ∴ DC = 2.1 cm.

Since,
AD is the bisector of ∠A meeting side BC at D in Δ ABC
Hence, Δ ABD ~ Δ ACD

Now,
⇒ $\frac{A B}{A C} = \frac{B D}{C D}$

⇒ $\frac{5}{4.2} = \frac{2.5}{C D}$

⇒ $5 \times C D = 2.5 \times 4.2$

⇒ $C D = 2.1 c m$

$∴$ DC = 2.1 cm.