 # G.G.51: Arcs Determined by Angles 2: Investigate theorems about the... intersecting a circle when the vertex is on the circle

```Regents Exam Questions G.G.51: Arcs Determined by Angles 2
Name: ________________________
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G.G.51: Arcs Determined by Angles 2: Investigate theorems about the arcs determined by angles
intersecting a circle when the vertex is on the circle
1 The new corporate logo created by the design
engineers at Magic Motors is shown in the
accompanying diagram.
2 The NUK Energy Company is designing a new
logo, as shown in the accompanying diagram, with
mNK = 130 and mNK = mNU .
What is the measure of ∠KNU ?
1) 50°
2) 65°
3) 80°
4) 100°
If chords BA and BC are congruent and
mBC = 140, what is m∠B?
1) 40
2) 80
3) 140
4) 280
3 In the accompanying diagram of circle O, AB and
BC are chords and m∠AOC = 96. What is
m∠ABC ?
1)
2)
3)
4)
1
32
48
96
192
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
Name: ________________________
www.jmap.org
4 In the diagram below, circle O has m∠ABC = z .
What is m∠AOC ?
1)
2)
3)
4)
6 In the diagram below of circle O, chords AD and
BC intersect at E.
z
2z
1
z
2
z2
Which relationship must be true?
CAE ≅ DBE
1)
AEC ∼ BED
2)
3) ∠ACB ≅ ∠CBD
4)
5 In the diagram below, quadrilateral JUMP is
inscribed in a circle..
CA ≅ DB
7 As shown in the diagram below, quadrilateral
DEFG is inscribed in a circle and m∠D = 86.
Opposite angles J and M must be
1) right
2) complementary
3) congruent
4) supplementary
Determine and state mGFE . Determine and state
m∠F .
2
Regents Exam Questions G.G.51: Arcs Determined by Angles 2
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8 In the diagram below of circle O, chords DF , DE ,
FG , and EG are drawn such that
mDF :mFE :mEG :mGD = 5 :2 :1 :7. Identify one
pair of inscribed angles that are congruent to each
other and give their measure.
9 A machine part consists of a circular wheel with an
inscribed triangular plate, as shown in the
accompanying diagram. If SE ≅ EA , SE = 10, and
mSE = 140, find the length of SA to the nearest
tenth.
3
Name: ________________________
ID: A
G.G.51: Arcs Determined by Angles 2: Investigate theorems about the arcs determined by angles
intersecting a circle when the vertex is on the circle
Answer Section
1 ANS: 1
. Equal chords intercept equal arcs. If
then
The measure of an inscribed angle is half that of its intercepted arc. So
REF: 080107b
2 ANS: 1
3
4
5
6
REF:
ANS:
ANS:
ANS:
ANS:
080803b
2
2
4
2
REF: 060802b
REF: fall9914b
REF: 011124ge
REF: 061026GE
1
ID: A
7 ANS:
86° ⋅ 2 = 172° 180° − 86° =94°
REF: 081432ge
8 ANS:
2
× 360 = 48. Since the chords forming ∠D and ∠G are
15
intercepted by FE , their measure is 24°. mGD = 7 × 360 = 168. Since the chords forming ∠E and ∠F are
15
∠D, ∠G and 24° or ∠E , ∠F and 84°. mFE =
intercepted by GD, their measure is 84°.
REF: fall0836ge
9 ANS:
then
6.8. Equal chords intercept equal arcs. If
And
The measure of an inscribed angle is half that of its intercepted arc. So
Draw altitude
which is half the length of
and use the cosine function to find the leg of the right triangle created,
.
.
REF: 080629b
2
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