let o be any interior point of an equilateral triangle ABC .Show that 2(OA+OB+OC)>3AB
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Answer:
2(OA + OB + OC) > 3AB
Step-by-step explanation:
Let o be any interior point of an equilateral triangle ABC .Show that 2(OA+OB+OC)>3AB
O is interior point of an equilateral triangle ABC
Three triangles are formed by O
ΔOAB , ΔOBC & ΔOCA
in any trinagle sum of two sides > third side
=>
in ΔOAB OA + OB > AB
in ΔOBC OB + OC > BC
& in ΔOCA OC + OA > AC
Adding all three
OA + OB + OB + OC + OC + OA > AB + BC + AC
ΔABC is equilateral => AB = BC = AC
=> 2OA + 2OB + 2OC > AB + AB + AB
=> 2(OA + OB + OC) > 3AB
QED
Proved
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