幸运28

Trying to Circle a Square

1. Here is a square ABCD with diagonal BD drawn: a. Construct a circle centered at A with radius AD. b. Construct a circle centered at C with radius CD. c. Draw the diagonal AC and write a conjecture about the relationship between the diagonals BD and AC. d. Label the intersection of the diagonals as point E and construct a circle centered at E with radius EB.   Submit a statement about the relationship between the diagonals and the circle.
2. Use your conjecture along with your straightedge and compass tools to construct a square inscribed in a circle.
Are you ready for more? Use straightedge and compass moves to construct a square that fits perfectly outside the circle, so that the circle is inscribed in the square. How do the areas of these 2 squares compare?