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AC+BD or the circumference of the circle

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AC+BD or the circumference of the circle [#permalink] New post   24 Nov 2020, 08:17
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GRE The circumference of the circle with center O.jpg
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Quantity A
Quantity B
AC+BD
The circumference of the circle with center O



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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swarna1143
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Re: AC+BD or the circumference of the circle [#permalink] New post   24 Nov 2020, 11:00
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option a says OA+OC+OB+OD and the sum is 4r (r is radius) and option B says 2 pai (3.1416) r.
now divide both sides by 2r. and u will be left with in A 2 and in B 3.1416 (pai). (dont know how to type pai) (sorry for that).
so. b is greater.
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Re: AC+BD or the circumference of the circle [#permalink] New post   27 Jan 2021, 09:19
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While there is no common information given about the circle and any of its components, the information given in statement 2 i.e. O is the centre of the circle is actually common information.

This helps us understand that AC and BD are the diameters of the given circle.

If the radius of the shown circle be 'r' units, then diameter = 2r units.

Quantity A = AC + BD = 2r + 2r = 4r units

Quantity B = Circumference of circle = 2*pi*r units = 6.28r units, since the approx value of pi = 3.14

Quantity B is always greater. The correct answer option should be B.

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Re: AC+BD or the circumference of the circle [#permalink] New post   27 Jan 2021, 12:29
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Something a little more visual: disconnect each radius from the center and point it toward the next point on the circle. It should be obvious that the straight distance is shorter than the curved one, so the circumference will always be the greater quantity.

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Re: AC+BD or the circumference of the circle [#permalink]
27 Jan 2021, 12:29
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