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ABC is an equilateral triangle, and point D is the midpoint of side BC

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Bunuel
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ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   11 Apr 2022, 01:30
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E

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31% (02:41) correct 69% (02:20) wrong based on 106 sessions
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ABC is an equilateral triangle, and point D is the midpoint of side BC. A is also a point on circle with radius r = 3. What is the area of the triangle?

(1) The line that passes through A and D also passes through the center of the circle.

(2) Including point A, the triangle intersects the circle at exactly four points.



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Boho
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Re: ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   11 Apr 2022, 06:04
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Statement (1) The line that passes through A and D also passes through the center of the circle.
Altitude can be any length between 0 and 6; Hence, area of triangle is not fixed- Not sufficient

Statement (2) Including point A, the triangle intersects the circle at exactly four points.

Multiple triangles can be formed - Not sufficient

Combined :

there is only one way in which AD = 6 will be the altitude of the triangle= sufficient

(C) is correct IMO
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ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   11 Apr 2022, 06:13
1) Multiple triangles are possible: Connect AD. Circle can be located anywhere along this line and can even be located external to this line (only intersects at A) => NOT SUFFICIENT

2) Multiple triangles are possible => NOT SUFFICIENT

E is the answer
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Re: ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   13 Apr 2022, 13:42
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Please take a look at option 2 explanation, on why it is insufficient!
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Re: ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   13 Apr 2022, 15:38
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circle touching a triangle at four points, simply can mean a circle's radius is smaller than any height? that's how i thought of it, meaning R=3 is useless.
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Re: ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   21 Apr 2022, 06:47
OE if possible, thanks
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Re: ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink] New post   05 Aug 2022, 12:55
Boho wrote:
Statement (1) The line that passes through A and D also passes through the center of the circle.
Altitude can be any length between 0 and 6; Hence, area of triangle is not fixed- Not sufficient.


Can u provide a pictorial representation of this plz, I am unable to visualize it.
Thanks in advance.

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Re: ABC is an equilateral triangle, and point D is the midpoint of side BC [#permalink]
05 Aug 2022, 12:55
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Bunuel
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