Q. 7 C5.0( 2 Votes )

# In ΔABC, B—M—C and A—N—C, ||. If NC : NA = 1 : 3 and CM = 4, then BC = ………..

A. 12

B. 16

C. 8

D. 1/2

Answer :

We have the diagram as,

Given: In ∆ABC,

MN ∥ AB

NC:NA = 1:3

⇒

CM = 4

To find: BC = ?

In ∆ABC,

Since, MN ∥ AB

⇒

⇒

⇒ MB = 4 × 3 [∵, ⇒ ]

⇒ MB = 12

In B – M – C,

BC = MB + CM

⇒ BC = 12 + 4

⇒ BC = 16

**Thus, option (b) is correct.**

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