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OpenStudy (anonymous):
Prove that sum of diagonals of a convex pentagon is greater than the perimeter but less than double the perimeter
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OpenStudy (kc_kennylau):
I'd use the triangles ABC, BCD, CDE, DEA and EAB.
OpenStudy (kc_kennylau):
AC>AB, BD>BC, ... Therefore AC+BD+... > AB+BC+...
OpenStudy (kc_kennylau):
But AC<AB+BC, BD<BC+CD, ... Therefore AC+BD+... < AB+BC+BC+CD+CD+DE+DE+EA+EA+AB = 2*perimeter
OpenStudy (anonymous):
thank u
OpenStudy (kc_kennylau):
No problem
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