Question

am is a midian of triangle ABC. prove that (ab+bc+ca) greater than 2am

Answer 1

in triangle ABM

AB +BM >AM [ The sum of 2 sides of a triangle is always greater than the third side] -1

now ,in triangle ACM

AC +CM.>AM [ The sum of 2 sides of a triangle is alwats greater than the third side] -2

adding 1 and 2

AB +BM +AC +CM >AM+AM

ABC >2AM

AB +BC +CA >2AM