How to Construct an Equilateral Triangle Inscribed Inside a Circle

Last Updated: March 28, 2021

While not a skill one would use in everyday life, knowing how to draw an inscribed triangle is needed in certain math classes. It's also a cool trick to impress your less mathematically inclined friends or family. This wikiHow will teach you how to construct one.

Steps

1
Draw the point at which your circle will be centered. Label this "Point O".
- It technically doesn't matter what letters you use to label your points. This article will choose names for the points in the images and refer to them as such to keep the instructions clear, but you may prefer to use different ones.
2
Use a compass to draw a perfect circle centered at point O. If you don't happen to have a drawing compass, you can make your own.

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3
Use a ruler to draw a vertical line straight through point O. Extend this line past the boundaries of your circle.
- To make sure that the vertical line goes exactly through the middle of the circle, place your pencil's tip at point O and then align the ruler with the pencil tip. The ruler will be slightly off-center but the line will not.
4
Draw the points at which the line intersects the circle. Label the bottom point "Point W" and the top point "Point X".
5
Draw a second circle. This circle will be centered at Point W and the radius will extend to Point O.
- It's okay if this circle goes off your paper. The important thing is that it intersects the first circle you drew twice.
6
Mark both places where the two circles intersect. Label the point on the left "Point Y" and the point on the right "Point Z".
7
Connect points X, Y, and Z using a ruler or straight edge.