How to Construct an Equilateral Triangle Inscribed Inside a Circle

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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 How.com.vn will teach you how to construct one.

  1. How.com.vn English: Inscribeatriangle1.png
    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. How.com.vn English: Inscribeatriangle2.png
    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. How.com.vn English: Inscribeatriangle4.png
    4
    Draw the points at which the line intersects the circle. Label the bottom point "Point W" and the top point "Point X".
  5. How.com.vn English: Inscribeatriangle5.png
    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.
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    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. How.com.vn English: Inscribeatriangle7.png
    7
    Connect points X, Y, and Z using a ruler or straight edge.
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      About This Article

      How.com.vn English: Joseph Meyer
      Reviewed by:
      Math Teacher
      This article was reviewed by Joseph Meyer. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. This article has been viewed 35,880 times.
      24 votes - 55%
      Co-authors: 5
      Updated: March 28, 2021
      Views: 35,880
      Categories: Drawing Shapes | Geometry
      Thanks to all authors for creating a page that has been read 35,880 times.

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