Circle Terminology & Practice

1. Always, Sometimes, Never: A tangent to a circle contains the diameter.

Always

Sometimes

Never

A tangent to a circle is a line that touches the circle at exactly one point. Since a diameter is a line segment that passes through the center of the circle and has both endpoints on the circle, it cannot be a tangent. Therefore, a tangent to a circle does not contain the diameter.

Explanation

A tangent to a circle is a line that touches the circle at exactly one point. Since a diameter is a line segment that passes through the center of the circle and has both endpoints on the circle, it cannot be a tangent. Therefore, a tangent to a circle does not contain the diameter.

2. Always, Sometimes, Never: A secant to the circle contains the diameter.

Always

Sometimes

Never

A secant to the circle may or may not contain the diameter. It depends on the position of the secant in relation to the circle. If the secant intersects the circle at two distinct points, then it contains the diameter. However, if the secant only intersects the circle at one point or does not intersect at all, then it does not contain the diameter. Therefore, the statement is sometimes true depending on the specific scenario.

Explanation

A secant to the circle may or may not contain the diameter. It depends on the position of the secant in relation to the circle. If the secant intersects the circle at two distinct points, then it contains the diameter. However, if the secant only intersects the circle at one point or does not intersect at all, then it does not contain the diameter. Therefore, the statement is sometimes true depending on the specific scenario.

3. Always, Sometimes, Never: A chord in a circle contains a radius.

Always

Sometimes

Never

A chord in a circle contains a radius sometimes because it depends on the position of the chord in relation to the center of the circle. If the chord is a diameter, it will always contain a radius. However, if the chord is not a diameter, it will not contain a radius. Therefore, the statement is sometimes true depending on the specific scenario.

Explanation

A chord in a circle contains a radius sometimes because it depends on the position of the chord in relation to the center of the circle. If the chord is a diameter, it will always contain a radius. However, if the chord is not a diameter, it will not contain a radius. Therefore, the statement is sometimes true depending on the specific scenario.

4. Which segment is tangent to the circle?

3

1 and 4

4

1,2, and 4

A segment is tangent to a circle if when you extend the segment to a line, it's an actual tangent to the circle. Notice in one place, "tangent" is used as an adjective, and in the other it's a noun.

Explanation

A segment is tangent to a circle if when you extend the segment to a line, it's an actual tangent to the circle. Notice in one place, "tangent" is used as an adjective, and in the other it's a noun.

5. Always, Sometimes, Never: Two concentric circles are similar.

Always

Sometimes

Never

All circles are similar because their radii are proportional.

Explanation

All circles are similar because their radii are proportional.

6. Always, Sometimes, Never: Two tangent segments to a circle are congruent.

Always

Sometimes

Never

They are congruent if they come from the SAME external point. Note that you could also have tangent segments that come from different external points, but the segments don't have to be congruent.

Explanation

They are congruent if they come from the SAME external point. Note that you could also have tangent segments that come from different external points, but the segments don't have to be congruent.