Regents Exam Questions G.G.52: Chords and Secants 1
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G.G.52: Chords and Secants: Investigate, justify, and apply theorems about arcs of
a circle cut by two parallel lines
1 In the diagram of circle O below, chords
the circle.
If
1)
2)
3)
4)
, what is
and
are parallel, and
is a diameter of
?
20
30
60
120
2 In the diagram of circle O below, chord
What is
1) 150
2) 120
3) 100
4) 60
?
is parallel to diameter
and
.
Regents Exam Questions G.G.52: Chords and Secants 1
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3 In the diagram below of circle O, diameter
If
1)
2)
3)
4)
, what is
is parallel to chord
?
110
70
55
35
4 In circle O shown in the diagram below, chords
If
1)
2)
3)
4)
.
and
38
44
88
96
, what is
?
and
are parallel.
Regents Exam Questions G.G.52: Chords and Secants 1
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5 In the diagram of circle O below, chord
What is
1) 35
2) 55
3) 70
4) 110
and
.
?
6 In the diagram of the circle below,
What is
1) 5
2) 10
3) 55
4) 80
is parallel to diameter
?
,
, and
.
Regents Exam Questions G.G.52: Chords and Secants 1
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7 Parallel secants
If
1)
2)
3)
4)
and
and
intersect circle O, as shown in the diagram below.
, then
equals
106
115
130
156
8 In the diagram below of circle O,
Which statement must be true?
1)
2)
3)
4)
, and
.
Regents Exam Questions G.G.52: Chords and Secants 1
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9 In the diagram below of circle O,
is parallel to
.
Which statement must be true?
1)
2)
3)
4)
10 In the diagram below of circle O, chord
at E and
at F.
Which statement must always be true?
1)
2)
3)
4)
is parallel to chord
. Chord
intersects
Regents Exam Questions G.G.52: Chords and Secants 1
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11 In the diagram of the circle shown below, chords
and
are parallel.
and
intersect at Q, and chords
Which statement must always be true?
1)
2)
3)
4)
12 Points A, B, C, and D are located on circle O, forming trapezoid ABCD with
Which statement must be true?
1)
2)
3)
4)
.
Regents Exam Questions G.G.52: Chords and Secants 1
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13 In the diagram below of circle O, chord
is parallel to chord
.
A correct justification for
in circle O is
1) parallel chords intercept congruent arcs
2) congruent chords intercept congruent arcs
3) if two chords are parallel, then they are
congruent
4) if two chords are equidistant from the center,
then the arcs they intercept are congruent
14 In the diagram below, two parallel lines intersect circle O at points A, B, C, and D, with
and
. Find
.
15 In the diagram below, trapezoid ABCD, with bases
with diameter
. If
, find
.
and
, is inscribed in circle O,
Regents Exam Questions G.G.52: Chords and Secants 1
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1 ANS: 2
Parallel chords intercept congruent arcs.
.
REF: 060906ge
2 ANS: 2
Parallel chords intercept congruent arcs.
REF: 080904ge
3 ANS: 3
.
.
.
REF: 061205ge
4 ANS: 2
Parallel chords intercept congruent arcs.
REF: 011302ge
5 ANS: 1
Parallel chords intercept congruent arcs.
REF: 081302ge
6 ANS: 4
REF: 011525ge
7 ANS: 2
Parallel secants intercept congruent arcs.
8
9
10
11
12
13
REF: 081503ge
ANS: 1
Parallel lines intercept congruent arcs.
REF: 061001ge
ANS: 1
Parallel lines intercept congruent arcs.
REF: 061105ge
ANS: 4
Parallel lines intercept congruent arcs.
REF: 081201ge
ANS: 3
Parallel lines intercept congruent arcs.
REF: 061409ge
ANS: 2
REF: 061516ge
ANS: 1
Parallel lines intercept congruent arcs.
REF: 081413ge
.
.
Regents Exam Questions G.G.52: Chords and Secants 1
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14 ANS:
.
REF: 011229ge
15 ANS:
REF: 081129ge