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How to Make a Triangle in a Circle With a Compass and a Ruler

An equilateral triangle -- one with sides of equal lengths as well as three identical angles -- is a basic shape in Euclidian geometry. The triangle's relationship with circles is significant because if it is drawn either encompassing a circle, or within a circle, it has the closest area to the circle of any other triangle. With a compass and ruler, you can draw a perfect equilateral triangle.

Things You'll Need

  • Drawing compass
  • Ruler
  • Paper
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Instructions

    • 1

      Draw a straight line down the paper.

    • 2

      Place the pointed tip of the compass on the line and rotate the compass around that center point, drawing a circle. (The circle can be of any size.) For clarity, label the points where the line and the circle intersect Point A and Point B.

    • 3

      Keeping the compass set to the same angle, place its tip on Point A with the drawing end of the compass on the edge of the circle. Turn the the compass to draw an arc between the edges of the circle.

    • 4

      Draw a straight line connecting the points where the arc intersects the circle.

    • 5

      Draw straight lines from the ends of the line you just drew to Point B, on the edge of the circle, to complete the triangle.

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