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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.

How are the diagonals related to the circle?

Use the knowledge you gained above and compass and straightedge moves to construct a square inscribed in a circle. Note: "inscribed" means the square will fit perfectly inside the circle.

Attribution

illustrative mathematics. geometry. unit 1. section 7. activity 3. "Trying to Circle a Square" https://im.kendallhunt.com/HS/teachers/2/1/7/index.html Licensed under the Creative Commons Attribution 4.0 license https://creativecommons.org/licenses/by/4.0/