All-American Gaming Logo
January 15th, 2019 at 7:34:24 PM
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All-American Gaming's logo consists of two equilateral triangles and a circle, as shown:
If AB has length 1, then what is the length of AO?
If AB has length 1, then what is the length of AO?
January 15th, 2019 at 10:34:02 PM
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Quote: ThatDonGuyAll-American Gaming's logo consists of two equilateral triangles and a circle, as shown:
If AB has length 1, then what is the length of AO?
half the square root of 21--I'm surprised how hard this problem is.
January 16th, 2019 at 6:44:44 PM
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Quote: ChesterDoghalf the square root of 21--I'm surprised how hard this problem is.
That's what I get as well. What surprised me was, the distance from A to where circle O is tangent to line AC is a rational number.
January 16th, 2019 at 9:30:17 PM
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Quote: ThatDonGuyQuote: ChesterDoghalf the square root of 21--I'm surprised how hard this problem is.That's what I get as well. What surprised me was, the distance from A to where circle O is tangent to line AC is a rational number.
That is interesting!
I looked for an easy way to see it. Think of a 60-degree rhombus with vertices (0, 0), (1, 0), (1/2, 31/2/2), and (3/2, 31/2/2). Then inscribe a circle in the rhombus. The center of the circle is at the midpoint of the line segment connecting (0, 0) and (3/2, 31/2/2), which is (3/4, 31/2/4).
So, that rational number distance between A and where circle O is tangent to line AC is 2 + 3/4 = 11/4.
(edit) I have the rhombus slanting toward the right, but in your diagram it slants to the left. So, the distance in your diagram would be 2+1/4 = 9/4.
I looked for an easy way to see it. Think of a 60-degree rhombus with vertices (0, 0), (1, 0), (1/2, 31/2/2), and (3/2, 31/2/2). Then inscribe a circle in the rhombus. The center of the circle is at the midpoint of the line segment connecting (0, 0) and (3/2, 31/2/2), which is (3/4, 31/2/4).
So, that rational number distance between A and where circle O is tangent to line AC is 2 + 3/4 = 11/4.
(edit) I have the rhombus slanting toward the right, but in your diagram it slants to the left. So, the distance in your diagram would be 2+1/4 = 9/4.
Last edited by: ChesterDog on Jan 16, 2019
