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705-805 (Hard)|   Geometry|      
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:34
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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85% (hard)

Question Stats:

46% (02:50) correct 54% (02:11) wrong based on 63 sessions

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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as shown in the figure above. The shaded region is what fraction of the area of triangle ACE ?
(1) ∠DFE = 90°
(2) The length of AF is \(10\sqrt{3}\)

Weekly Quant Quiz #4 Ques 8

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A
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:41
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as shown in the figure above. The shaded region is what fraction of the area of triangle ACE ?
(1) ∠DFE = 90°
(2) The length of AF is 103‾√

C
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:48
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THe answer to this question could be (A) . Please find my solution attached.

Regards,
GLadi
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 10:50
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Statement 1:
We know Angle DEF = 60, Angle DFE=90 so Angle EDF = 30. This basically gives us the ratio of sides DF:FE:ED = Sqrt3:1:2. From this we can derive the ratio of the sides of the Bigger triangle. And we can easily get the area of the shaded region.

Eliminate B, C, E.

Statement 2:
Tells only about AF and nothing about any other sides or angles. So there might be many triangles with this length of AF.
Insufficient.

Answer = A
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Oct 2018, 11:11
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(1) ∠DFE = 90° .......NS........ will not get the area
(2) The length of AF is 10root 3 .......NS...... will not get the area

1+2) can calculate all the areas of the trangles.....thus Suff Ans C
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 13 Sep 2019, 06:28
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Gladiator59
THe answer to this question could be (A) . Please find my solution attached.

Regards,
GLadi
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howw long did u take to solve this question
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Equilateral triangle BDF is inscribed in equilateral triangle ACE, as 04 Jul 2023, 18:05
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