Consider a triangle ABC, the respective middles A, B, C of sides BC, CA, AB, and center of gravity G. (a)Show that AA +BB +CC = 3/2 (GA+GB +GC). (b)Show the nequality GA + GB + GC BC +CA+AB/2 . Deduce the inequality: AA + BB + CC 3/4 (BC + CA+AB). (c) Let N be the symmetric of point A with respect to poi

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Consider a triangle ABC, the respective middles A, B, C of sides BC, CA, AB, and center of gravity G. (a)Show that AA +BB +CC = 3/2 (GA+GB +GC). (b)Show the nequality GA + GB + GC > BC +CA+AB/2 . Deduce the inequality: AA + BB + CC > 3/4 (BC + CA+AB). (c) Let N be the symmetric of point A with respect to point A. What order relationship exists in triangle ABN between sides AN and the sum of the other two sides? Deduce the inequality: AA < AB + AC /2 , then the inequality: AA + BB + CC < BC +CA+AB.

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