im.g.1.7.3.Trying to Circle a Square

Topic:
Circle, Square

Instructions

1. Here is 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.

 Write a conjecture about the relationship between the diagonals BD and AC.

d. Label the intersection of the diagonals as point E. (To do this, select the point and use the Style Bar to rename it.) Then construct a circle with center at E and radius EB.

Are You Ready for More?

Use the tools in the applet 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 two squares compare?