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Answers
Given : O is the centre of the circle of diameter d
To Find : which is bigger, 3d or the perimeter of ΔABC
Solution:
Sum of two sides of triangle is greater than third side
in ΔAOB
OA + OB > AB
in Δ BOC
OB + OC > BC
in Δ AOC
OA + OC > AC
Adding all three
OA + OB + OB + OC + OC + OA > AB + BC + AC
OA = OB = OC = Radius = diameter/2 = d/2
=> d/2 + d/2 +d/2 +d/2 +d/2 +d/2 > AB + BC + AC
=> 3d > AB + BC + AC
AB + BC + AC = perimeter of ΔABC
=> 3d > perimeter of ΔABC
3d is bigger than perimeter of ΔABC
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Answer:
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