# Trying to Circle a Square

- Author:
- Anthony Gillman

- Topic:
- Circle, Constructions, Geometry, 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?