Circle Blueprint Reference Sheet
Circle Geometry Reference
Spring 2026 Revision
Measures
Circumference \(C = 2\pi r\) or \(\pi d\)
Arc Length \(L = \frac{m\overparen{AB}}{360} \cdot 2\pi r\)
Area \(A = \pi r^2\)
Basic Angles
Central Angle \(m\angle = \text{arc}\)
Inscribed Angle \(m\angle = \frac{1}{2}\text{arc}\)
Inscribed Poly Opp \(\angle\)'s sum to 180°
Intersections
Vertex INSIDE
\(x = \frac{1}{2}(\text{arc}_1 + \text{arc}_2)\)
x
Vertex OUTSIDE
\(x = \frac{1}{2}(\text{big arc} - \text{small arc})\)
x
R
Radius \(\perp\) Tangent at the point of tangency (90°).
D
Inscribed \(\angle\) facing a diameter is always exactly 90°.
Standard Formula Reference G.CI.1-4
Circle Test Form F Student Work
Circle Geometry Test
Form F | Spring 2026
Name:
G.CI.1: / 13
Date:
G.CI.3: / 31
Class:
Total: / 44
Question 1 (6 pts)
Circle O: SN and MT are diameters. Angle SOT = 62°, Angle NOR = 30°. WT and WV are tangent lines.
O T S N M R W V
arc MR =
arc NR =
arc MST =
arc ST =
arc TSR =
Angle OTW =
Question 2 (7 pts)
Identify each circle part in circle O using the diagram below.
O A B C D E F G Line H
Radius:
Diameter:
Tangent Line:
Chord:
Secant Line:
Point of Tangency:
Center:
3. Inscribed Angle (3 pts)
Given inscribed \(\angle ACB = 72^\circ\) and arc \(BC = 110^\circ\).
arc AB =
arc AC =
A B C 72° 110°
4. Find x and y (2 pts)
arc = 156° x y
x:
y:
5. Find x and y (2 pts)
70° 90° x y
x:
y:
6. Vertex Outside (3 pts)
18° 105° y x
x:
y:
7. Diameters (3 pts)
BD and CE are diameters.
arc DC =
arc ED =
B D C E A 125°
8. Find x & arc AC (3 pts)
A B C 55° arc AB=150° arc AC = 11x - 10 110°
x:
arc AC:
9. Find x & y (3 pts)
A B C 240° x y
arc x:
angle y:
10. Central Angle (2 pts)
A B O x 108°
Given arc AB = 108°
x =
11. Central Angles (2 pts)
A 35° 82° 158° C D
Angle CAD:
Arc CD:
12. Inscribed Quadrilateral (2 pts)
\( \angle ABC = \)
arc ADC =
C D A B arc BC=120° arc CD=100° arc AD=80°
13. Inscribed Triangle (3 pts)
Diameter LN
x =
arc LM =
L M N arc LM: 12x - 4 arc MN: 8x + 4
14. Circumference (2 pts)
a) r = 9cm
b) d = 18cm
15. Arc Length (1 pt)
r = 10cm, central angle = 72°.
Length:
Bonus Challenge
G is an external vertex formed by secant lines GAC and GDB. Chords AC and BE intersect inside at I. F is the center. Arcs: \(BE=70^\circ, EC=80^\circ, AC=100^\circ, AD=70^\circ, DB=40^\circ\).
I G F A B C D E
\(\angle BFC = \)
\(\angle BIE = \)
\(\angle BAC = \)
\(\angle AGC = \)
\(\angle DEC = \)
\(\angle BCE = \)
Circle Test Form F Answer Key
Answer Key: Circle Test Form F
Teacher Reference Only
Questions 1 - 3
1. Circle Measures
Arc MR = 150°, Arc NR = 30°, Arc MST = 242°, Arc ST = 62°, Arc TSR = 210°, ∠OTW = 90.0°
2. Identifying Parts
Radius: OA, OB, or OD; Diameter: AD; Tangent Line: Line H; Chord: CE; Secant Line: FG; Tangency: B; Center: O
3. Inscribed Angles
Arc AB = 144° (72 × 2); Arc AC = 106° (360 - 110 - 144)
Questions 4 - 7
4. Tangent-Chord
x = 78° (156/2), y = 102° (180-78)
5. Vertex Inside
x = 80° ([90+70]/2), y = 100° (180-80)
6. Vertex Outside
y = 69° (minor arc intercepted), x = 18° (vertex angle measure)
7. Diameters
Arc DC = 55° (180-125), Arc ED = 125° (Vertical angle Arc BC = 125)
Questions 8 - 11
8. Inscribed Algebra
Arc AC = 100°, x = 10 (Using Angle A=55, Arc BC=110, Arc AB=150; 11x-10 = 100)
9. Secants Outside
x = 120° (Minor Arc = 360-240), y = 60° (Vertex Angle = [240-120]/2)
10. Central Angle
x = 108° (Central angle = intercepted arc measure)
11. Central Angles
Angle CAD = 82°, Arc CD = 82° (Central angle = intercepted arc)
Questions 12 - 15
12. Inscribed Quad
∠ABC = 90° (Arc ADC = 100+80=180; 180/2), Arc ADC = 180°
13. Inscribed Diameter
x = 9 (12x-4 + 8x+4 = 180), Arc LM = 104°
14. Circumference
a) 18π cm (r=9); b) 18π cm (d=18)
15. Arc Length
4π cm ≈ 12.57 cm (Using r=10, θ=72°)
Bonus Challenge Solutions
Arcs: BE=70, EC=80, AC=100, AD=70, DB=40. Points A, D, B, E, C in order.
BFC: 150° (BE+EC)
BIE: 95° ( [AB+EC]/2 )
BAC: 75° ( 150/2 )
AGC: 40° ( [CB-AD]/2 )
DEC: 85° ( [DA+AC]/2 )
BCE: 35° ( 70/2 )
