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?