Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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Name: __________________________________
G.G.51: Arcs Determined by Angles: Investigate theorems about the arcs
determined by angles intersecting a circle when the vertex is on the circle
1 Circle O with
What is the ratio of
1)
2)
3)
4)
and
is shown in the diagram below.
to
2 In the diagram below, circle O has
1) z
2) 2z
3)
4)
?
. What is
?
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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3 In the diagram below of circle O,
What is the
1) 12
2) 24
3) 48
4) 60
?
4 In the accompanying diagram of circle O,
is
?
1)
2)
3)
4)
32
48
96
192
.
and
are chords and
. What
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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5 As shown in the diagram below,
If
1)
2)
3)
4)
, then
is a diameter of circle O, and chord
is drawn.
is
40
70
110
140
6 The new corporate logo created by the design engineers at Magic Motors is shown in the
accompanying diagram.
If chords
1) 40
2) 80
3) 140
4) 280
and
are congruent and
, what is
?
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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7 The NUK Energy Company is designing a new logo, as shown in the accompanying
diagram, with
and
.
What is the measure of
1) 50°
2) 65°
3) 80°
4) 100°
?
8 In the diagram below, quadrilateral JUMP is inscribed in a circle..
Opposite angles J and M must be
1) right
2) complementary
3) congruent
4) supplementary
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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9 In the diagram below of circle O, chords
and
intersect at E.
Which relationship must be true?
1)
2)
3)
4)
10 As shown in the diagram below, quadrilateral DEFG is inscribed in a circle and
.
Determine and state
. Determine and state
.
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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11 In the diagram below of circle O, chords
,
,
, and
are drawn such that
. Identify one pair of inscribed angles that are congruent
to each other and give their measure.
12 A machine part consists of a circular wheel with an inscribed triangular plate, as shown in
the accompanying diagram. If
,
, and
, find the length of
to
the nearest tenth.
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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1
2
3
4
5
6
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
2
2
3
2
1
1
REF:
REF:
REF:
REF:
REF:
061322ge
fall9914b
011523ge
060802b
081518ge
. Equal chords intercept equal arcs. If
then
The measure of an inscribed angle is half that of its intercepted arc. So
REF: 080107b
7 ANS: 1
REF: 080803b
8 ANS: 4
9 ANS: 2
REF: 061026GE
10 ANS:
REF: 081432ge
REF: 011124ge
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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11 ANS:
,
and 24° or
,
and 84°.
intercepted by
, their measure is 24°.
intercepted by
, their measure is 84°.
. Since the chords forming
. Since the chords forming
and
are
and
are
REF: fall0836ge
12 ANS:
6.8. Equal chords intercept equal arcs. If
then
And
The measure of an inscribed angle is half that of its intercepted arc. So
Draw altitude
which is half the length of
REF: 080629b
and use the cosine function to find the leg of the right triangle created,
.
.