Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
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Exercise 1 Page 581

How can you use two chords to draw a diameter? Be aware that a diameter is also a chord.

See solution.

Practice makes perfect
We have previously used a carpenter's square to draw the diameter of a circular piece of wood. Since the tool is used to draw right angles, we drew a right angle on the wood. By the Inscribed Right Triangle Theorem, the hypotenuse of the right triangle that was formed is the diameter.
Now, let's think about what other tools we can use to draw the diameter. Let's think about relationship between a chord and a diameter. This relationship can be explained by the Converse Perpendicular Chord Bisector Theorem.

Converse Perpendicular Chord Bisector Theorem

If one chord of a circle is the perpendicular bisector of another chord, then the first chord is a diameter.

We will first draw a chord and find its perpendicular bisector, which is a diameter. To do so, we need a straightedge and a compass. Let's draw a chord on the wood.
The perpendicular bisector of this chord will be the diameter of the circular wood. To draw it, we place the tip of the compass on one of the endpoints of the chord. Then, we open the compass beyond the midpoint, and draw an arc. We then place the tip on the other endpoint and draw another arc. We repeat this procedure for a different amplitude of the compass.
Finally, we draw the line that connects intersection of the arcs drawn.
We have drawn the diameter of the circle. We could use a straightedge and a compass to draw the diameter.