# Circle Terminology & Practice

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Quizzes Created: 5 | Total Attempts: 17,437
Questions: 10 | Attempts: 629

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Test your knowledge of chords, tangents, arcs, etc.

• 1.

### Which figure shows a chord?

• A.

B

• B.

C

• C.

A

• D.

A and B

• E.

A, B and C

D. A and B
Explanation
A chord is a segment whose endpoints are ON the circle.

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• 2.

### Which segment is tangent to the circle?

• A.

3

• B.

1 and 4

• C.

4

• D.

1,2, and 4

C. 4
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.

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• 3.

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

• A.

Always

• B.

Sometimes

• C.

Never

B. Sometimes
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.

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• 4.

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

• A.

Always

• B.

Sometimes

• C.

Never

C. Never
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.

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• 5.

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

• A.

Always

• B.

Sometimes

• C.

Never

B. Sometimes
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.

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• 6.

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

• A.

Always

• B.

Sometimes

• C.

Never

B. Sometimes
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.

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• 7.

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

• A.

Always

• B.

Sometimes

• C.

Never

A. Always
Explanation
All circles are similar because their radii are proportional.

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• 8.

### Assume the segment that looks tangent is tangent. Find CB.

• A.

2

• B.

10

• C.

4

C. 4
Explanation
Connect points A and D to make a right triangle with hypotenuse between D and B. AD = 6 (why?). Pythagorean Theorem.

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• 9.

### Assume the segment that looks tangent is tangent. Find the radius of the circle.

• A.

Cannot be determined with given information.

• B.

4

• C.

5

C. 5
Explanation
Let PQ and MP both equal "x". Set up the Pythagorean Theorem.

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• 10.

• A.

30

• B.

55

• C.

25