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.