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In a δAbc, Ad is the Bisector of ∠A, Meeting Side Bc at D. If Bd = 2.5cm, Ab = 5cm and Ac = 4.2cm, Find Dc. - Mathematics

In a ΔABC, AD is the bisector of ∠A, meeting side BC at D.

If BD = 2.5cm, AB = 5cm and AC = 4.2cm, find DC.

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Solution

We have,

∠BAD = ∠CAD

We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

`therefore"BD"/"DC"="AB"/"AC"`

`rArr2.5/"DC"=5/4.2`

`rArr"DC"=(2.5xx4.2)/5`

`=(25xx42)/(5xx100)=(5xx42)/100=210/100=2.1 `cm

∴ DC = 2.1 cm

Concept: Angle Bisector
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.3 | Q 1.1 | Page 31
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