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A
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Difficulty:
5%
(low)
Question Stats:
90% (01:29) correct
10%
(01:52)
wrong
based on 265
sessions
History
Date
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A. 40
B. 140
C. 20
D. 90
I solved this question but...
my approach differs from what Manhattan had done and so I need some clarification, please.
What I did was:
1. Given that area of circle is 180 and that BE, CD are both diameters
2. I found the area of ACB sector using the angle 40% and got it as 20 sq.units
3. I then figured out BAD area by 90 - 20 (because C-B-D-C is a semi circle)
4. I then figured out ACE area by 90 - 20 (because C-B-E-C is a semi circle)
5. I then figured out ADE area by 90 - 70 (because C-D-E-C is a semi circle)
so, the total is 20 + 20 = 40
However, Manhattan says "The two central angles, CAB and DAE, describe a total of 80°."
What I do NOT understand is, how can we say that Angle EAD = Angle BAC ?
Is it something like, when two diameters intersect, the opposite angles formed by them are equal? I am not sure of this but looks like could have saved a few seconds in solving this.
EDIT: FOUND IT! Angle EAD = Angle BAC because vertical angels are equal. The next chapter "Lines & Angles" gave it away
What I did was:
1. Given that area of circle is 180 and that BE, CD are both diameters
2. I found the area of ACB sector using the angle 40% and got it as 20 sq.units
3. I then figured out BAD area by 90 - 20 (because C-B-D-C is a semi circle)
4. I then figured out ACE area by 90 - 20 (because C-B-E-C is a semi circle)
5. I then figured out ADE area by 90 - 70 (because C-D-E-C is a semi circle)
so, the total is 20 + 20 = 40
However, Manhattan says "The two central angles, CAB and DAE, describe a total of 80°."
What I do NOT understand is, how can we say that Angle EAD = Angle BAC ?
Is it something like, when two diameters intersect, the opposite angles formed by them are equal? I am not sure of this but looks like could have saved a few seconds in solving this.
EDIT: FOUND IT! Angle EAD = Angle BAC because vertical angels are equal. The next chapter "Lines & Angles" gave it away
08 Jan 2014, 04:17
Kudos
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flower07
BE and CD are both diameters of circle with center A (see figure). If the area of Circle A is 180 units^2, what is the area of sector ABC + sector ADE?
Angle BAC and angle DAE are equal, so together sector ABC and sector ADE comprise 80 degrees sector and its area is 80/360*180=40 square units.
Answer: A.
08 Jan 2014, 16:56
Kudos
Bookmarks
[quote="flower07"]
A. 40
B. 140
C. 20
D. 90
ABC = ADE = 80/360
80/360 reduces to 2/9
2 = x
9 180
Cross multiply (180*2) and (9*x)
360 = 9x
..9....9
x = 40
Attachment:
Untitled.png
BE and CD are both diameters of circle with center A (see figure). If the area of Circle A is 180 units^2, what is the area of sector ABC + sector ADE?A. 40
B. 140
C. 20
D. 90
ABC = ADE = 80/360
80/360 reduces to 2/9
2 = x
9 180
Cross multiply (180*2) and (9*x)
360 = 9x
..9....9
x = 40
