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Question
In the given figure, ∠AMN = ∠MBC = 76° . 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.
Solution
Sol:
In ΔAMN and ΔABC
∠𝐴𝑀𝑁 = ∠𝐴𝐵𝐶 = 76° (𝐺𝑖𝑣𝑒𝑛)
∠𝐴 = ∠𝐴 (𝐶𝑜𝑚𝑚𝑜𝑛)
By AA similarity criterion, ΔAMN ~ ΔABC
If two triangles are similar, then the ratio of their corresponding sides are proportional
∴` (AM)/(AB)=(MN)/(BC)`
⇒ `(AM)/(AM+MB)=(MN)/(BC)`
⇒ `a/(a+b)=(MN)/c`
⇒ `MN=(ac)/(a+b)`
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