Important Note: The method I explain below only works because I happened to get lucky drawing the triangle. See further down this thread for a way that does actually work
I needed to saw a disc (actually a wargames base) in two equal halves, but it didn’t have a clear centre point visible on it.
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Here’s how to do it. First, draw a triangle whose points are on the disc’s circumference:
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Make this as large as you can, meaning it’ll be approximately equilateral — though there’s no need to make the corners exactly 60°. Just eyeballing it will be accurate enough. (You could draw the triangle much narrower, but you’ll make things easier for yourself if you don’t
)
Next, from each of the triangle’s corners, draw a line that’s at a 90° angle to the opposite side:
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These three lines should all cross the same point: the so-called
orthocenter of the triangle. Because the triangle’s points are on its circumference, this coincides with the centre of the disc.
In my case I just had to saw straight through that to get two halves:
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but you could of course also use it to drill a hole for an axle, glue something dead centre, or for anything else that requires you to find the middle of a circle.
(With the added note that for cutting a disc in halves, you don’t even need to draw six lines: three will do. Draw two sides of the triangle and then the third line from one of the “open” corners to the line opposite. This will go through the centre of the disc if you do it right. It’s just that it’s easier to spot errors if you do draw all six lines, because you can see whether the ones in the middle all go through the same point.)
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