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BE and CD are both diameters of circle with center A (see fi

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BE and CD are both diameters of circle with center A (see fi  [#permalink]

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New post Updated on: 08 Jan 2014, 03:18
4
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (01:25) correct 10% (01:57) wrong based on 99 sessions

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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

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 :)

Originally posted by flower07 on 07 Jan 2014, 22:43.
Last edited by Bunuel on 08 Jan 2014, 03:18, edited 1 time in total.
Renamed the topic and edited the question.
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Re: BE and CD are both diameters of circle with center A.  [#permalink]

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New post 08 Jan 2014, 03:17
flower07 wrote:
BE and CD are both diameters of circle with center A (see figure in the attachment). If the area of Circle A is 180 units2, what is the area of sector ABC + sector ADE1

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 :)


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?
Image

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.
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Re: BE and CD are both diameters of circle with center A (see fi  [#permalink]

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New post 08 Jan 2014, 15:56
[quote="flower07"]
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
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Re: BE and CD are both diameters of circle with center A.  [#permalink]

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New post 08 Jan 2014, 22:45
1
Bunuel wrote:
flower07 wrote:
BE and CD are both diameters of circle with center A (see figure in the attachment). If the area of Circle A is 180 units2, what is the area of sector ABC + sector ADE1

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 :)


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?
Image

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.



% anle subtended by the arc= % of area occupied by the arc
hence arc ABC and arc ADE together subtend an angle of 80
area occupied by these arcs = (80/360)*180=40
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Re: BE and CD are both diameters of circle with center A (see fi  [#permalink]

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New post 01 Jul 2019, 08:16
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Re: BE and CD are both diameters of circle with center A (see fi   [#permalink] 01 Jul 2019, 08:16

BE and CD are both diameters of circle with center A (see fi

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