Circle Terminology & Practice
Test your knowledge of chords, tangents, arcs, etc.
Questions and Answers
- 1.
Which figure shows a chord?
- A.
B
- B.
C
- C.
A
- D.
A and B
- E.
A, B and C
Correct Answer
D. A and BExplanation
A chord is a segment whose endpoints are ON the circle.Rate this question:
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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
Correct Answer
C. 4Explanation
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.Rate this question:
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- 3.
Always, Sometimes, Never: A secant to the circle contains the diameter.
- A.
Always
- B.
Sometimes
- C.
Never
Correct Answer
B. SometimesExplanation
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.Rate this question:
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- 4.
Always, Sometimes, Never: A tangent to a circle contains the diameter.
- A.
Always
- B.
Sometimes
- C.
Never
Correct Answer
C. NeverExplanation
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.Rate this question:
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- 5.
Always, Sometimes, Never: A chord in a circle contains a radius.
- A.
Always
- B.
Sometimes
- C.
Never
Correct Answer
B. SometimesExplanation
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.Rate this question:
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- 6.
Always, Sometimes, Never: Two tangent segments to a circle are congruent.
- A.
Always
- B.
Sometimes
- C.
Never
Correct Answer
B. SometimesExplanation
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.Rate this question:
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- 7.
Always, Sometimes, Never: Two concentric circles are similar.
- A.
Always
- B.
Sometimes
- C.
Never
Correct Answer
A. AlwaysExplanation
All circles are similar because their radii are proportional.Rate this question:
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- 8.
Assume the segment that looks tangent is tangent. Find CB.
- A.
2
- B.
10
- C.
4
Correct Answer
C. 4Explanation
Connect points A and D to make a right triangle with hypotenuse between D and B. AD = 6 (why?). Pythagorean Theorem.Rate this question:
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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
Correct Answer
C. 5Explanation
Let PQ and MP both equal "x". Set up the Pythagorean Theorem.Rate this question:
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- 10.
Assume the segments that look tangent are tangent. Find m
- A.
30
- B.
55
- C.
25
Correct Answer
C. 25Explanation
The angles in a quadrilateral sum to 360. Once you solve for x, plug in to find D.Rate this question:
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.jpg "Assume the segment that looks tangent is tangent. Find the radius of the circle.")
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Mar 21, 2023Quiz Edited by
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Apr 09, 2011Quiz Created by
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