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# The circle above has area 25.

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The circle above has area 25. [#permalink]  20 Sep 2018, 16:35
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54% (00:48) correct 45% (00:28) wrong based on 66 sessions
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The circle above has area 25.JPG [ 18.71 KiB | Viewed 1138 times ]

The circle above has area 25.

 Quantity A Quantity B The length of chord AB $$10$$

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.
[Reveal] Spoiler: OA

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Re: The circle above has area 25. [#permalink]  21 Sep 2018, 07:04
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Expert's post
sandy wrote:
Attachment:
Capture.JPG

The circle above has area 25.

 Quantity A Quantity B The length of chord AB $$10$$

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.

Area of circle = πr² (where r = radius)

So, we can write: πr² = 25
Approximate π to write: 3r² ≈ 25 [yes, we often use 3.14 as the approximation for π, but you'll see why 3 works just as well]
Divide both sides by 3 to get: r² ≈ 25/3
Simplify: r² ≈ 8.3333...
So, r ≈ √8.33333

Since √9 = 3, we know that √8.33333 is less than 3
This means the radius is less than 3, which means the DIAMETER is less than 6
So, the greatest possible length of chord AB is still less than 6

We get:
Quantity A: some number less than 6
Quantity B: 10

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Re: The circle above has area 25. [#permalink]  18 Jan 2019, 16:13
Even the dia is 7 it is less than 10 hence B
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Re: The circle above has area 25. [#permalink]  07 Sep 2019, 06:24
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Since we our given an area we can use that to find the diameter of the circle. We know that the chord of a circle will always be <= the diameter of the circle. Using the diameter and this known relationship we can then compare A and B.
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daum_equation_1567866147931.png [ 112.95 KiB | Viewed 1104 times ]

Re: The circle above has area 25.   [#permalink] 07 Sep 2019, 06:24
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