In ΔABC, M ∈ AB, N ∈ AC such that MN || BC. ...... is not true.select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) AN MB = AM • NC
(b) AM•MB = AN • NC
(c) AB • AN = AM·AC
(d) AB • NC = AC.MB
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given: in ∆ABC, MN || BC
according to property of triangles , we can say that AM/MB = AN/NC
(AM + MB)/MB = (AN + NC)/NC
AB/MB =AC/NC
MB/AB = NC/AC
Cross multiplication of the above equations,
⇒ AM × NC = AN × MB
Or AM . NC = AN . MB is true.
AM × AC = AN × AB
Or AM . AC = AN . AB is true.
MB × AC = NC × AB
Or MB . AC = NC . AB is true.
So, AM . MB = AN . NC is not true.
Thus, option (b) is correct.
according to property of triangles , we can say that AM/MB = AN/NC
(AM + MB)/MB = (AN + NC)/NC
AB/MB =AC/NC
MB/AB = NC/AC
Cross multiplication of the above equations,
⇒ AM × NC = AN × MB
Or AM . NC = AN . MB is true.
AM × AC = AN × AB
Or AM . AC = AN . AB is true.
MB × AC = NC × AB
Or MB . AC = NC . AB is true.
So, AM . MB = AN . NC is not true.
Thus, option (b) is correct.
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