Exercise 1 Page 588

Practice makes perfect

We want to classify BG as specifically as possible.

Let's review some important definitions about circles.

Radius: A segment whose endpoints are the center and any point on the circumference on a circle.
Chord: A segment whose endpoints are on the circumference of a circle.
Diameter: A chord that contains the center of the circle.
Secant: A line that intersects a circle in two points.
Tangent: A line in the plane of a circle that intersects the circle in exactly one point — the point of tangency.

We can see that BG has its endpoints on the circumference of a circle and it does not contain the circle's center. Therefore, it is a chord.

Next we are going to classify CD.

The segment has one endpoint in the center and one on the circumference of the circle. From we definitions we reviewed in Part A, we know that the segment is a radius.

We have been asked to classify AD.

This segment has its endpoints on the circumference of the circle and it contains the center. That is equivalent to the definition of a diameter.

Let's have a look at FE.

A circle with a center C and points A, B, D, E, F, and G in clockwise order, starting from the leftmost point of the circle. There is a diameter labeled AB, a chord labeled BG that intersects AB in the point, which is closer to A than to B. The chord EF is red. The entire figure is drawn in black lines on a white background, except for the red segment.

Let's classify this segment! It has its endpoints on the circumference of the circle and does not contain the center. Therefore, we know that it is a chord.

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Exercises p.588-589

Exercise 1 Page 588

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