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The perimeter of ∆ABC

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The perimeter of ∆ABC [#permalink] New post   22 Sep 2018, 09:13
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Quantity A
Quantity B
The perimeter of ∆ABC
The circumference of the circle


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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B
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MateusLima30
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Re: The perimeter of ∆ABC [#permalink] New post   22 Sep 2018, 11:18
Could you explain how to approach this type of question? I marked B, the correct answer, by learning from a mistake on a previous questions you just posted. However, I did not completely get it. Should I just assume that anything inscribed has a smaller perimeter than the object in which it is inscribed?
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Re: The perimeter of ∆ABC [#permalink] New post   23 Sep 2018, 01:26
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You have to consider the simple fact the straight line such as the triangle's side AB is always inferior to the relative arc AB.

So, sides AB + BC + AC < Arc AB + Arc BC + Arc AC.

Therefore, the quantity A (sides) is < the quantity B (arcs).

B > A.

B is the answer.

Hope this helps.

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Re: The perimeter of ∆ABC [#permalink] New post   18 Jan 2019, 08:51
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sum of arcs > sum of chords

Hence B
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The perimeter of ABC [#permalink] New post   13 Aug 2022, 11:18
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Let's consider a circle with a circumference of 4π, thus diameter = 4.

If it was possible to build an equilateral triangle with 3 diameters in length (each side) within the circle (biggest possible chord), then its perimeter would be 3x2 = 6.
But the circumference is 4π > 12. So it must be the case that B > A.
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