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Finding the Center of a Circle
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Finding the Center of a Circle

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“Just relax. Find your center.”

Caddyshack (1980)

It seems like a pretty simple task, doesn’t it? I bet a lot of people (myself included) are confident that they can eyeball a good center point. But eyeballing isn’t exact and sometimes you need to be exact. So how does one find an exact center on an existing circle? It’s actually not very difficult and there are multiple ways to do it. Here are a few of the simplest methods.

Method 1: Chords

First, let’s define a “chord.” A chord is any straight line whose endpoints are both on a circle. (The infinite line extension of a chord is called the secant line. Not relevant for this, but something to know.) This method is probably the simplest.

Start by drawing a chord through your circle anywhere. Using a ruler, measure the chord and find its exact center point. Draw a perpendicular line there. Repeat the process elsewhere within the circle. The point where both of your perpendicular lines meet is your center. You can repeat the process as many times as you’d like to be absolutely on point.

Method 2: Carpenter Square

The second method will involve using a carpenter’s square. If you don’t have one, you can use anything with a perfect 90 degree angle, even a sheet of paper. You’ll want something like a ruler for drawing your lines perfectly straight, though.

Draw an “L” shape, making sure that all of your points intersect the circle. Using your square, draw a third line parallel to one of lines you already drew. You should end up with a square that only has 3 sides drawn. Draw an “X” within your makeshift box, where each line intersects your circle, and the point at which the two lines intersect will be your center.

Method 3: Carpenter Square + Ruler

If you have both a carpenter square and a ruler, this is one of the fastest ways to find your center. Place the square so that the corner is on the edge of your circle. Lay your ruler over the square, lining up the edge of the ruler with the two other points that the square touches the circle. Draw your line. Rotate the square and repeat.

Method 4: Carpenter Square and Triangle

This method will likely be your fastest if you happen to have both tools available. Lay your square along the OUTSIDE of the circle this time. Line your triangle up over the longer side of your square and make sure the angle of your triangle is right on the corner of your square. Draw a line. Rotate and repeat.