Card 1 of 20
EasyStudy card 1
Prompt
In one circle, what follows from congruent arcs?
Answer
Their corresponding chords are congruent.
MathChapter 19: Circles
Flashcards
Arcs and Chords Flashcards
Twenty concise cards on chord theorems and the center-distance right triangle.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
In one circle, what follows from congruent chords?
Answer
Their corresponding minor arcs are congruent.
Card 3 of 20
EasyStudy card 3
Prompt
What does a diameter perpendicular to a chord do?
Answer
It bisects the chord and its intercepted arc.
Card 4 of 20
EasyStudy card 4
Prompt
What is true of chords equidistant from the center?
Answer
They are congruent.
Card 5 of 20
EasyStudy card 5
Prompt
What is the converse equidistant-chord fact?
Answer
Congruent chords are equidistant from the center.
Card 6 of 20
EasyStudy card 6
Prompt
What right-triangle formula connects radius, chord, and center distance?
Answer
\(d^2+(c/2)^2=r^2\).
Card 7 of 20
EasyStudy card 7
Prompt
Why does the formula use c/2?
Answer
The perpendicular center segment bisects the chord.
Card 8 of 20
MediumStudy card 8
Prompt
After solving for a half-chord, what final check is needed?
Answer
Double it if the question asks for the full chord.
Card 9 of 20
MediumStudy card 9
Prompt
What is the longest possible chord in radius-r circle?
Answer
The diameter, \(2r\).
Card 10 of 20
MediumStudy card 10
Prompt
Radius 13 and chord 10 give what center distance?
Answer
12.
Card 11 of 20
MediumStudy card 11
Prompt
Radius 10 and center distance 8 give what chord?
Answer
12.
Card 12 of 20
MediumStudy card 12
Prompt
Equal center distances are measured in what direction?
Answer
Perpendicularly from center to each chord.
Card 13 of 20
MediumStudy card 13
Prompt
May the full chord be used as a right-triangle leg?
Answer
No; one triangle contains half the chord.
Card 14 of 20
MediumStudy card 14
Prompt
What information links curved arcs to straight chord lengths?
Answer
Congruence in the same or congruent circles.
Card 15 of 20
MediumStudy card 15
Prompt
Does this lesson require power-of-a-point products?
Answer
No; use only the stated chord theorems and right-triangle model.
Card 16 of 20
MediumStudy card 16
Prompt
How do you test whether a proposed chord is possible?
Answer
Verify its length is at most the diameter.
Card 17 of 20
HardStudy card 17
Prompt
Radius 25 and chord 30 give what center distance?
Answer
20.
Card 18 of 20
HardStudy card 18
Prompt
A chord's halves are 4x+1 and 7x-20. Find x.
Answer
7.
Card 19 of 20
HardStudy card 19
Prompt
Equal-distance chords: one is 42. What is the other?
Answer
42.
Card 20 of 20
HardStudy card 20
Prompt
Two equal parallel chords lie on opposite sides, each 20 from center. Separation?
Answer
40.
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