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505-555 Level|   Geometry|               
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Bunuel
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The rectangle is equally placed on the center of the circle.
Let O be the center of the circle.
And X be the midpoint of AB.
Then OX = 5/2 = 2/5 and XB = 12/2 = 6
Triangle OXB is a right angles triangle.
OB = radius = \(\sqrt{6^2+2.5^2} = \sqrt{42.5}\)

Area = \(π*r^2 = 42.5π\)

B is the answer.
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diagonal of figure ; 13
so radis - 6.5
area = 6.5^2 * pi = 42.25 pi
IMO B
Bunuel

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00π
B. 42.25π
C. 64.00π
D. 84.50π
E. 169.00π


PS77502.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1231.png
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Solution





Given:
    • ABCD is a rectangle.

To Find:
    • Area of circle.

Approach and Working:


    • Since ABCD is a rectangle, \(AC^2\) = \(AB^2\) + \(BC^2\)
      o \(AC^2\) = \(12^2\) + \(5^2\) = 144 +25 = 169
         AC = 13

    • ∆ ABC is a right triangle and by applying the property that angle in a semi-circle is 90 degrees.
      o We can conclude that AC is the diameter of the triangle.
      o Hence, radius of circle = \(\frac{13}{2}\)

    • Therefore, area of circle = π * \((\frac{13}{2})^2\) = (\(\frac{169}{4}\)) π =42.25 π

Hence, option B is the correct answer.

Correct Answer: B
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Bunuel

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00π
B. 42.25π
C. 64.00π
D. 84.50π
E. 169.00π

Attachment:
2019-04-26_1231.png

We see that diagonal AC (of the rectangle) is also the diameter of the circle. When we make diagonal AC, we see that we create a right triangle, and more specifically a 5-12-13 right triangle, so the length of AC is 13.

Since the diameter is 13, the radius is 6.5, and the area of the circle is (6.5)^2 x π = 42.25π.

Answer: B
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Bunuel

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00π
B. 42.25π
C. 64.00π
D. 84.50π
E. 169.00π


PS77502.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1231.png

A good solution of the above question:

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Diagonal of ABCD = 13 (Using Pythagoras theorem)

Hence, Diameter of circle = Diagonal = 13 | Radius = 6.5

Area of circle = pi * r^2 = pi * (13/2) * (13/2) = 42.25 pi
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Bunuel

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00π
B. 42.25π
C. 64.00π
D. 84.50π
E. 169.00π


PS77502.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1231.png

Draw a line connecting points A and C.

An important circle property (see video below for more info) tells us that, if we have a 90-degree inscribed angle, then that angle must be containing ("holding") the DIAMETER of the circle.
So, we know that AC = the diameter of the circle.


To find the hypotenuse of the red triangle, we can EITHER apply the Pythagorean Theorem OR recognize that 5 and 12 are part of the Pythagorean triplet 5-12-13

With either approach, we learn that AC = 13

IMPORTANT: if the diameter (AC) is 13, then the radius = 13/2 = 6.5

What is the area of the circular region?
Area of circle = πr²
So, area = π(6.5²)
= 42.25π

Answer: B

RELATED VIDEO FROM MY COURSE

can u plz clear this ?
the angle formed by diameter at circum is 90 degrees

but here we know angle is 90 degree so we are saying thtt chor di diamerter
so my qsn is ,is collary also true?
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Hi vanam52923,

Yes - the corollary is ALSO true. If you have a right triangle inscribed in a circle, then the hypotenuse of the triangle is the diameter of the circle.

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The diagonal of the rectangle is the diameter of the circle because the half triangle is the right angle.
So, diameter = 13
radius = 13/2
area of circle = pi r*r = 169/4 pi = 42.25pi
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Bunuel

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00π
B. 42.25π
C. 64.00π
D. 84.50π
E. 169.00π


PS77502.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1231.png


The Pythagorean triplets formula \(5:12:13\) is applied here. \(So, \ the \ Hypotenuse \ or \ Diameter \ is \ 13.\)

Radius\( = \frac{13}{2}=6.5\)

The area of the circular region\(=πr^2=π(6.5)^2=42.25π\)

The answer is \(B. \)
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Bunuel

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

A. 36.00π
B. 42.25π
C. 64.00π
D. 84.50π
E. 169.00π


PS77502.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1231.png

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Answer: Option B

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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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