# Measure diameter from 3 points

How do I measure what the dimaeter is for the 3 read points on the
attached. The red points are 3 lugs to fit in to a round hole.
I am not entirely sure what your question is, but I think that the answer is probably to Google "circle equilateral triangle inscribed".
if you know the lenghts of the 3 sides of the triangle , you can get the radius of the circle using the law of sines : 2R = abc / 2S
where S is the area of the triangle, you can get it with S = sqrt [p(p?a)(p?b)(p?c)]
p is the half perimeter of the triangle.
I think.
Owain
if that is an /equilateral/ triangle it's easier: radius is the side of the triangle divided by SQRT(3)
see e.g. the "circumscribed circle" at
I'm puzzled by the diagram. The red dots seem to be at some arbitrary position within the circle. You can calculate the radius/diameter of the circle which just touches those three points, but I don't see how that tells you the diameter of the circle shown in your diagram.
from 3 points> will get you the answer
Ignore the outer circle the 3 Red dots are plastic lugs that push in to a hole but I need to determine what diameter the hole would be. The 3 dots are an equilateral triangle each side being 23.5 mm.
I will check for an online calculator.
measure between any two red points
multiply that distance by cos60° for diameter
This might assist:
On the otherhand I would find the equidistant lines from each pair of points and where they intersect that would be the centre. Then measure from the centre to one of the points to get the radius, double to get the diameter:
Do you need the real, four point contact circle, or can we treat the squares as points?
If the latter, then if the side of the triangle is s, the circle diameter is s times sqrt(3) over 2
If not, you need to know the size of the squares too.
It is similar to the image below the 3 plastic lugs push fit in to a round hole, there is a tolerence of around 3 mm so the squares can be treated as points.

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