How to Cut a Circle Into Three Equal Circles Using Parallel Lines

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Cutting a circle into three equal circles requires you to stick very closely to the literal definition of the term "circle." Cut a circle into three equal circles using parallel lines with help from a longtime mathematics educator in this free video clip.

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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to cut a circle into three equal circles using parallel lines. Well, the fact of the matter is, cutting a circle into three equal circles is going to be kind of difficult because drawing three circles that encompass an entire circle is going to be a little bit on the difficult side because it's going to be some loss of pieces of the original circle. But, if you want to cut a circle into three equal parts, then that, that can definitely be arranged. Now, here's the formula that you want to keep in mind to do that. It's going to be r squared times, and then you have theta minus sine theta over two equals to pie r squared over three. Now, this formula on the right hand side looks kind of familiar because the area of a circle is pie r square and because you're dividing by three. What that tells you here is if you're trying to divide the circle into three equal parts, each equal part is going to have one third the area of the original circle. So, that's why it's pie r squared over three. Now, we want to do after this is solve and get the r squares on the same side and then just use a little bit of Algebra and, and go from there. And once you have the formula in a lot more simplified form, what you want to do is draw two diagonals on the circle and of course, make sure that the diagonals are parallel. So, what the formula up there helps ensure is giving your theta and your r what would you have to do on the circle to be able to draw the diagonals in a way that they're parallel to each other and you'll have three equal parts of the circle. So, as long as your formula, follow this formula and the strategy, you will be good to go. So, I'm Jimmy Chang and that's how to create three equal parts, not circle, but three equal parts of a circle using parallel lines.


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