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Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively,

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Bunuel
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Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   29 Mar 2019, 02:04
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Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, such that angle BAE = angle ACD. Let F be the intersection of segments AE and CD, and suppose that triangle CFE is equilateral. What is angle ACB?

(A) 60°
(B) 75°
(C) 90°
(D) 105°
(E) 120°
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C
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Archit3110
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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   29 Mar 2019, 08:21
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Bunuel wrote:
Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, such that angle BAE = angle ACD. Let F be the intersection of segments AE and CD, and suppose that triangle CFE is equilateral. What is angle ACB?

(A) 60°
(B) 75°
(C) 90°
(D) 105°
(E) 120°


draw fig as per given info
we shall get angle BAE= 30 = angle ACD
and angle FCE= 60
so angle ACB = 90
IMO C
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PgRaul
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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   29 Dec 2020, 20:27
https://artofproblemsolving.com/wiki/in ... /Problem_8
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CEdward
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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   17 Feb 2021, 20:15
I drew it as follows. Wondering what I did wrong...I got E as the answer...
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frankgraves
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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   18 Feb 2021, 01:03
Bunuel wrote:
Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, such that angle BAE = angle ACD. Let F be the intersection of segments AE and CD, and suppose that triangle CFE is equilateral. What is angle ACB?

(A) 60°
(B) 75°
(C) 90°
(D) 105°
(E) 120°


I got C but I did not use the information of "Triangle ABC has AB = 2*AC"
Now I am wondering what is the use of that information, can you tell me Bunuel ?
Thank you.
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ShaikhMoice
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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   14 Sep 2021, 11:26
Archit3110 wrote:
Bunuel wrote:
Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, such that angle BAE = angle ACD. Let F be the intersection of segments AE and CD, and suppose that triangle CFE is equilateral. What is angle ACB?

(A) 60°
(B) 75°
(C) 90°
(D) 105°
(E) 120°


draw fig as per given info
we shall get angle BAE= 30 = angle ACD
and angle FCE= 60
so angle ACB = 90
IMO C



How did you get this.
Thanks in advance
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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink] New post   13 Jul 2023, 09:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Triangle ABC has AB = 2*AC. Let D and E be on AB and BC, respectively, [#permalink]
13 Jul 2023, 09:47
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