Construction problem 1
Construct a rectangle with compasses and a straightedge.
Solution 1
Drawing a circle and two lines that are diagonals of a rectangle
1. Draw a circle O and two lines that pass through the center O.
2. Let A, B, C, and D be the four intersections on the circle O, as shown below, and draw lines between them. Then the quadrilateral ABCD forms a rectangle.
Solution 2
Drawing four circles to determine the four vertices of a rectangle
1. Draw a circle O and a circle P both of which with the same radii, so that they intersect each other at two points. And let Q and R be the two intersections.
2. Draw a circle Q and a circle R both of which with the same radii, so that the circle O and the circle Q intersect each other.
3. Let A, B, C, and D be the four intersections of circles, as shown below, and draw lines between them. Then the quadrilateral ABCD forms a rectangle.
Solution 3
Drawing two pairs of concentric circles
1. Draw a circle O and a circle P both of which with the same radii.
2. Draw a concentric circle O and a concentric circle P both of which with the same radii, so that the smaller circle O and the larger circle P intersect each other at two points.
3. Let A, B, C, and D be the four intersections of smaller circles and larger circles, as shown below, and draw lines between them. Then the quadrilateral ABCD forms a rectangle.
Mathematical Problems