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AB + AC  > 2 AD

Construct a parallelogram from ΔABC by drawing CE parallel to AB and BE parallel to AC. Now extend AD to join E.  AE is the diagonal and we know in a parallelogram the diagonals bisect each other.

Since AEC is a triangle,  sum of two sides is more than the third side

AC + CE > AE,                    CE = AB  and AE = 2 AD

AC + AB > 2 AD

hence the result

1 5 1
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