Constructing a square inscribed in a circle

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See also the animated version.

  After doing this Your work should look like this
  Start with the given circle, center O.

If the circle center point is not given, you can construct the center using the method shown in Finding the center of a circle.
1 Mark a point A on the circle. This will become one of the vertices of the square.
2 Draw a diameter line from the point A, through the center and on to cross the circle again, creating point C.
3 Set the compass on A and set the width to a little more than the distance to O.
4 Draw an arc above and below O.
5 Move the compass to C and repeat.
6 Draw a line through where the arc pairs cross, making it long enough to touch the circle at top and bottom, creating the new points B and D.

This is a diameter at right angles to the first one AC.
7 Draw a line between each successive pairs of points A, B, C, D
Done. ABCD is a square inscribed in the given circle.
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Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions