Question

In ∆ABC, a line parallel to the side BC intersects the sides AB and AC in
points M and N respectively. AM=8, MB=12, AN=6. Find NC.


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Answer 1

Explanation:

In △APQ and △ABC,

∠A is common.

∠APQ=∠ABC ...[corresponding angles]

∠AQP=∠ACB ...[corresponding angles]

∴△APQ∼△ABC ...(By AAA)

So, once the triangles are similar, their corresponding sides would be proportional.

AB

AP

=

AC

AQ

Hence proved.