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Q.

In ΔABC, A−B−C, A−N−C and MN ∥ BC , if MN=3 and BC=7, that divides AB from A in ratio ______

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a

3:7

b

4:7

c

3:4

d

4:3

answer is C.

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Detailed Solution

Triangles ABC and AMN congruent
Hence,
⇒∠BAC = MAN............(1)
we know that angle A is a common angle for both of the triangles ABC and AMN hence,
⇒∠AMN = ∠ABC.........(2)
So, we can say that triangle ABC and AMN are congruent
⇒ ΔABC ≅ ΔAMN.....................(3)

\Rightarrow \frac{AM}{AB} = \frac{MN}{BC}

……………………….(4)
We know MN = 3 and BC = 7,
⇒ MN/BC = 3/7
⇒ AM/AB = 3/7

\Rightarrow \frac{AB}{AM} = \frac{7}{3} \dots \dots \dots \dots \dots \dots (5)

We know AB = AM + BM

\Rightarrow \frac{AM + BM}{AM} = \frac{7}{3}

\Rightarrow 1 + \frac{BM}{AM} = \frac{7}{3}

\Rightarrow \frac{BM}{AM} = \frac{7}{3} - 1

\Rightarrow \frac{BM}{AM} = \frac{7 - 3}{3}

\Rightarrow \frac{BM}{AM} = \frac{4}{3}

Hence, AM:BM = 3:4
Therefore option (3) is correct.

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