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# An isosceles triangle with one angle of 120° is inscribed in

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Joined: 18 Dec 2017
Posts: 1136
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: An isosceles triangle with one angle of 120° is inscribed in  [#permalink]

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13 Jul 2019, 13:01
chetan2u wrote:
mau5 wrote:
An isosceles triangle with one angle of 120° is inscribed in a circle of radius 2. This triangle is rotated 90° about the center of the circle. What is the total area covered by the triangle throughout this movement, from starting point to final resting point?

A. $$\frac{4\pi}{3}$$

B. $$\frac{8\pi}{3}$$

C. $$4\pi$$

D.$$\frac{4\pi}{3}$$$$-\sqrt{3}$$

E.$$\frac{25\pi}{12}$$$$-\sqrt{3}$$

Manhattan GMAT challenge of the week.

Hi all,
Its a tough Q to be able to come up with exact answer in exactly 2 mins untill you visualize it. thereafter it becomes easy...
Trial : i think a bit of trial and we can be close to the correct answer..
Given that the iso tri has one angle as 120. so we can safely assume this triangle is inscribed on one side of the diameter.
Total area of circle=4pi.. the triangle rotates through 90 degree... so traversed area should be between pi and 2 pi approximately..
only E fits in...
for the exact answer, a sketch is reqd visualizing the triangle making a circle of radius 1 as it rotates and i'll explain after sometime as office time...

I would totally take this explanation and make peace with it. I did figure out triangle will be on one side of diameter, calculated total area of circle just couldn't think of 90/360 will make area traversed between pi and 2pi. Not bad though. Thank you Sir
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Joined: 27 Mar 2017
Posts: 119
Re: An isosceles triangle with one angle of 120° is inscribed in  [#permalink]

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24 Jan 2020, 03:24
luyennguyen wrote:
A. approximately 4
B. approx. 8
C. Approx. 12
D. Approx. 2
E. Approx. 5
S the triangle is less than 4. if it rotates 180 degree, max total S=8. If it rotates 90 degree, the S= 2/3*8 = approx.5 ( E)

Why is the triangle less than 4 units ?
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Joined: 27 Mar 2017
Posts: 119
Re: An isosceles triangle with one angle of 120° is inscribed in  [#permalink]

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24 Jan 2020, 03:25
chetan2u wrote:
mau5 wrote:
An isosceles triangle with one angle of 120° is inscribed in a circle of radius 2. This triangle is rotated 90° about the center of the circle. What is the total area covered by the triangle throughout this movement, from starting point to final resting point?

A. $$\frac{4\pi}{3}$$

B. $$\frac{8\pi}{3}$$

C. $$4\pi$$

D.$$\frac{4\pi}{3}$$$$-\sqrt{3}$$

E.$$\frac{25\pi}{12}$$$$-\sqrt{3}$$

Manhattan GMAT challenge of the week.

Hi all,
Its a tough Q to be able to come up with exact answer in exactly 2 mins untill you visualize it. thereafter it becomes easy...
Trial : i think a bit of trial and we can be close to the correct answer..
Given that the iso tri has one angle as 120. so we can safely assume this triangle is inscribed on one side of the diameter.
Total area of circle=4pi.. the triangle rotates through 90 degree... so traversed area should be between pi and 2 pi approximately..
only E fits in...
for the exact answer, a sketch is reqd visualizing the triangle making a circle of radius 1 as it rotates and i'll explain after sometime as office time...

Can you please explain the highlighted part.
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Re: An isosceles triangle with one angle of 120° is inscribed in  [#permalink]

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24 Jan 2020, 03:28
altairahmad wrote:
luyennguyen wrote:
A. approximately 4
B. approx. 8
C. Approx. 12
D. Approx. 2
E. Approx. 5
S the triangle is less than 4. if it rotates 180 degree, max total S=8. If it rotates 90 degree, the S= 2/3*8 = approx.5 ( E)

Why is the triangle less than 4 units ?

For another explanation of this question please click the link below

https://gmatclub.com/forum/an-isosceles ... l#p1534951
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Re: An isosceles triangle with one angle of 120° is inscribed in   [#permalink] 24 Jan 2020, 03:28

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# An isosceles triangle with one angle of 120° is inscribed in

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