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Question

In the given figure, ∠AMN = ∠MBC = 760 If p, q and r are the lengths of AM, MB and BC respectively, then express the length of MN in terms of p, q and r.

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Solution

In △AMN and △ABC
∠AMN = ∠ABC = 760 (Given)
∠A = ∠A (Common)
By AA similarity criterion, △AMN ∼ △ABC
If two triangles are similar, then the ratio of their corresponding sides are proportional
AMAB=MNBC
AMAM+MB=MNBCaa+b=MNcMN=aca+b

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