Exercise 18 Page 559

We have been given a circular piece of wood that needs to be cut into two semicircles. To do so, we will use a carpenter's square that is a L-shaped tool used to draw right angles. Note that we need to cut the circular piece of wood through its diameter to have two semicircles. We will decide how to use a carpenter's square in this situation. Remember that the Inscribed Right Triangle Theorem (Theorem $10.12)$ explains the relation between a right angle and a diameter in a circle. Let's recall it!

Inscribed Right Triangle Theorem

If a right triangle inscribed in a circle, then the hypotenuse is a diameter. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.

Therefore, by this theorem we will first place the inner corner of the carpenter's square on the outer edge of the circular wood. Then, we will draw two segments through the inner sides of the carpenter's square. Finally, by connecting the endpoints of the segments we can draw a diameter.