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On circle O, points C and D are on the same side of diameter AB, angle

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On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

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New post 27 Mar 2019, 20:39
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A
B
C
D
E

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Question Stats:

100% (02:11) correct 0% (00:00) wrong based on 21 sessions

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On circle O, points C and D are on the same side of diameter AB, angle AOC = 30°, and angle DOB = 45°. What is the ratio of the area of the smaller sector COD to the area of the circle?

(A) 2/9
(B) 1/4
(C) 5/18
(D) 7/24
(E) 3/10

Attachment:
6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png
6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png [ 10.64 KiB | Viewed 357 times ]

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Re: On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

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New post 27 Mar 2019, 20:54
Bunuel wrote:
Image
On circle O, points C and D are on the same side of diameter AB, angle AOC = 30°, and angle DOB = 45°. What is the ratio of the area of the smaller sector COD to the area of the circle?

(A) 2/9
(B) 1/4
(C) 5/18
(D) 7/24
(E) 3/10

Attachment:
6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png


The area of the smaller sector = pir^2((angle between the chord)/360)

Angle COD = 180 - 75 = 105

the ratio of the area of the smaller sector COD to the area of the circle = pir^2((angle between the chord)/360)/pir^2 ==> 105/360 ==> 7/24

Hence D
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Re: On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

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New post 27 Mar 2019, 20:54
\(\angle COD = 105^{\circ}\)

Area of sector COD = \(\frac{\angle COD}{360^{\circ}}*\pi*r^2\) ; where r is the radius of the circle.
Area of circle = \(\pi*r^2\)

\(\frac{Area of sector}{Area of circle}\) = \(\frac{\frac{\angle COD}{360^{\circ}}*\pi*r^2}{\pi*r^2}\)

=\(\frac{105^{\circ}}{360^{\circ}}\)

= \(\frac{7}{24}\)

OPTION: D
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Re: On circle O, points C and D are on the same side of diameter AB, angle  [#permalink]

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New post 28 Mar 2019, 02:23
Bunuel wrote:
Image
On circle O, points C and D are on the same side of diameter AB, angle AOC = 30°, and angle DOB = 45°. What is the ratio of the area of the smaller sector COD to the area of the circle?

(A) 2/9
(B) 1/4
(C) 5/18
(D) 7/24
(E) 3/10

Attachment:
6ef568ce45b5abd28fca3d7565af0a5d7af4c6f2.png


√COD = 105
and let radius of circle = 2 ; area = 4*pi
so
area of sector COD= 105/360 * 4*pi = 105/90 *pi
ratio
105/90 * pi / 4*pi
IMO D 7/24
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Re: On circle O, points C and D are on the same side of diameter AB, angle   [#permalink] 28 Mar 2019, 02:23
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On circle O, points C and D are on the same side of diameter AB, angle

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