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Given in `Delta ABC` ,AD is a median <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_IX_C07_S01_044_S01.png" width="80%"> <br> Constrution <br> Produce AD to a point E such that AD=DE and join CE <br> TP prove ` AC+AB gt 2 AD ` <br> Proof in `Delta ABD and Delta ECD ` <br> AD =DE [by construction ] <br> BD =CD [given AD is the median ] <br> `anngle ADB = angle CDE` [vertically opposite angle ] <br> `therefore Delta ABD cong Delta ECD ` [by SAS congruence rule ] <br> `rArr AB= CE ` [by CPCT ] <br> Now in `Delta AEC ,` <br> `AC+EC gt AE ` [Sum of two sides of a triagle is grater than the third side ] <br> `therefore AC+AB gt 2AD ` [from Eq. (i) and also taken that AD=AE ]