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The circle with center O

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The circle with center O [#permalink] New post 27 Dec 2016, 08:24
Expert's post
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Question Stats:

83% (00:38) correct 16% (00:20) wrong based on 12 sessions
Image

The circle with center O has a radius of 5

Quantity A
Quantity B
The perimeter of ABC
24


A)The quantity in Column A is greater.
B)The quantity in Column 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 with center O [#permalink] New post 27 Dec 2016, 11:02
Expert's post
Carcass wrote:
Image

The circle with center O has a radius of 5

Quantity A
Quantity B
The perimeter of ABC
24



First, if the circle has a radius of 5, then the DIAMETER = (2)(5) = 10

Since angle B holds (contains) the circle's diameter, we can conclude that angle B = 90 degrees.
This means that triangle ABC is a RIGHT triangle.

We know that the hypotenuse (diameter) = 10
And we know the length of the leg AB = 8
So, let's let x = the length of the missing leg (side BC)

Applying the Pythagorean Theorem, we can write: x² + 8² = 10²
Simplify: x² + 64 = 100
So, x² = 36, which means x = 6

We get:
Quantity A: 10 + 8 + 6
Quantity B: 24

Simplify to get:
Quantity A: 24
Quantity B: 24

Answer: C

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Re: The circle with center O   [#permalink] 27 Dec 2016, 11:02
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