| Given the midpoint C of a line segment AB, construct a line parallel to AB passing through a given point D using ruler only. |
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| Given the midpoint C of a line segment AB, construct a line parallel to AB passing through a given point D using ruler only. |
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| The straight lines l and m are parallel, construct the midpoint of A and B on m using ruler only. |
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| Through the point A lying outside the given straight line l and m, draw a straight line parallel to the given ones using ruler only. |
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| Given A, B on m and l parallel to m, construct C on m with AB = BC using ruler only. |
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| Given a circle and its center, construct an inscribed square using ruler only. |
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| Given two points, construct its midpoint using the compass alone. |
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| Construct the inversion of a point with respect to a circle using the compass alone. (You may assume the point lies outside the circle.) |
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| Construct the inversion of a straight line with respect to a circle using the compass alone. (You may assume the line lies outside the circle.) |
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| Let circle A passes through the center of circle B. Construct the inversion of A with respect to B using the compass alone. (Find two distinct points of the inversion.) |
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| Suppose that circle A does not pass through the center of circle B. Construct the inversion of A with respect to B using the compass alone. |
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| Construct the circumcircle of a triangle using the compass alone. |
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| Given a circle but not its center, find its center using the compass alone. |
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| Construct the vertices of a regular pentagon using the compass alone. |
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