Math Help Needed!

[Derek Arita]

OK geniuses...I have an equilateral triangle that is 20" from point to point to point. If I draw a circle that hits all three points, what's the diameter of the circle?
If I spent some time online looking for the formulas, I might be able to figure this out, but I know you guys are geniuses, so, solve for X, please.
Oh...I have an upright compressor with 3 feet. I want to put it on a square pad and need to know what dimensions to make the square.

[Patrick Varley]

The term you're looking for is "circumscribed". See here (https://www.mathopenref.com/trianglecircumcircle.html) for an explanation. In the case of an equilateral triangle, the radius = side/square root(3). In your case, that would be 11.547. Closest reasonable fraction would be 11 17/32. (35/64 will get you closer, though I've always found measuring anything less than 32nds to be a waste of time).

[Derek Arita]

See...I knew someone here would have it. So, with a radius of 11.547", the diameter would be approximately 23". If I make a square pad of 23" x 23", I should be good. Thanks so much, Patrick!

[John K Jordan]

See...I knew someone here would have it. So, with a radius of 11.547", the diameter would be approximately 23". If I make a square pad of 23" x 23", I should be good. Thanks so much, Patrick!

As usual, someone programed a calculator for this and put it on a web page: https://keisan.casio.com/exec/system/1223429573

Another way to figure your pad size is do draw the triangle on a big piece of paper, poster board, plywood, or floor. Then measure to see what size of pad makes sense based perhaps on the material and how much extra space you want outside the air compressor feet. Or pretend centimeters are inches and draw it out on a smaller piece of paper.

JKJ

[Derek Arita]

As usual, someone programed a calculator for this and put it on a web page: https://keisan.casio.com/exec/system/1223429573

Another way to figure your pad size is do draw the triangle on a big piece of paper, poster board, plywood, or floor. Then measure to see what size of pad makes sense based perhaps on the material and how much extra space you want outside the air compressor feet. Or pretend centimeters are inches and draw it out on a smaller piece of paper.

JKJ
John, what another great idea! I never thought of that. Thank you.

[David L Morse]

Yes, that triangle will fit a 23.1" circle. But it will also fit a 19.32" square. (20" times cos(15°))

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[Jack Frederick]

I'd bisect each of the 60 degree angles and draw lines from the point to the intersection of the 3 angles. From the intersection measure to the outside or let your compass do the walking.

[David Buchhauser]

OK geniuses...I have an equilateral triangle that is 20" from point to point to point. If I draw a circle that hits all three points, what's the diameter of the circle?
If I spent some time online looking for the formulas, I might be able to figure this out, but I know you guys are geniuses, so, solve for X, please.
Oh...I have an upright compressor with 3 feet. I want to put it on a square pad and need to know what dimensions to make the square.

Hi Derek,
Here is a "simple" formula that will work for any equilateral triangle inscribed in a circle. So you can use this to calculate the circle diameter for any size equilateral triangle.
David

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[Derek Arita]

Thanks David and thanks all for the help. I just couldn't get my mind to go there, but I knew you guys could.:D