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Home » In the given figure, ∠ AMN = ∠ MBC = . If p, q and r are the lengths of AM, MB and BC respectively then express the length of MN of terms of P, q and r.
In the given figure, ∠ AMN = ∠ MBC = 76^{\circ}. If p, q and r are the lengths of AM, MB and BC respectively then express the length of MN of terms of P, q and r.
CBSE | Class 10 | Exercise 4E | Maths | RS Aggarwal | Triangles
In the given figure, ∠ AMN = ∠ MBC = 76^{\circ}. If p, q and r are the lengths of AM, MB and BC respectively then express the length of MN of terms of P, q and r.

 

 

 

 

Answer:

In ∆AMN and ∆ABC,

∠???????????? = ∠???????????? =76^{\circ}

∠???? = ∠???? (????????????????????????)

By AA similarity criterion,

∆AMN ~ ∆ABC

If two triangles are similar, then the ratio of their corresponding sides are proportional.

\frac{A M}{A B}=\frac{M N}{B C}

\frac{A M}{A M+M B}=\frac{M N}{B C}

\frac{a}{a+b}=\frac{M N}{C}

\therefore M N=\frac{a c}{a+b}

 

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