The Big Angle/Segment Formula Review Sheet
Types of lines:
Circle Terminology
Term
Tangent
Secant
Chord
Diameter
Radius
Arc
Definition
Line that intersects the
circle exactly once
Line that intersects the
circle exactly twice
Line segment whose 2
endpoints meet the
edge of the circle
Segment whose 2
endpoints meet the
edge of the circle AND
cross through the
centerpoint
Segment whose
endpoints meet the
edge of the circle AND
the centerpoint
A portion of the
Circumference
Angle Properties
Vertex IN Circle
(CENTER)
Central Angle Property
Angle = Arc
Vertex OUTSIDE
circle
Vertex ON circle
x=x
Chord-Tangent Angle Property
Inscribed Angle
(Two-Chord) Property
Angle = ½ Arc
Angle = ½ Arc
Two Secants
(Intersecting Outside)
𝒙° =
1 Secant & 1 Tangent
(Intersecting Outside)
𝟏
(𝒃𝒊𝒈 𝒂𝒓𝒄 − 𝒔𝒎𝒂𝒍𝒍 𝒂𝒓𝒄)
𝟐
𝒙=
𝟏
(𝒃 − 𝒂)
𝟐
𝒙° =
𝟏
(𝒃𝒊𝒈 𝒂𝒓𝒄 − 𝒔𝒎𝒂𝒍𝒍 𝒂𝒓𝒄)
𝟐
𝒙=
𝟏
(𝒃 − 𝒂)
𝟐
Two Tangents
(Intersecting Outside)
𝒙° =
𝟏
(𝒃𝒊𝒈 𝒂𝒓𝒄 − 𝒔𝒎𝒂𝒍𝒍 𝒂𝒓𝒄)
𝟐
Vertex IN Circle
(NOT center)
2 Chord / 2 Tangent Property (Cross inside)
𝒙° =
𝟏
(𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒂𝒓𝒄 + 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕𝒆𝒅 𝒂𝒓𝒄)
𝟐
𝟏
𝒙° = (𝒂° + 𝒃°)
𝟐
𝒙=
𝟏
(𝒃 − 𝒂)
𝟐
Segment Properties
Intersecting
Chords
Theorem
c
b
𝑎∙𝑏 =c∙𝑑
a
d
𝑤
Intersecting
Secants
Theorem
𝑥(𝑥 + 𝑤) = 𝑦(𝑦 + 𝑧)
x
z
y
Intersecting
Tangent &
Secant
t
z
Intersecting
Tangents
𝑡 2 = 𝑦(𝑦 + 𝑧)
y
t
𝑡=𝑠
s
Special notes:
• Diameters/Radii that form Right Angles with chords BISECT them (cut them in
half)
• A tangent line is perpendicular to the radius at the Point of Tangency.
• If a circle is IN a polygon, all sides form tangents with the sides
• Chords equidistant are equal AND Equal Chords are equidistant.