Geometry Ch. 12 Flashcards
concentric circles-
concentric circles share the same center point in the same plane
radius
the radius is the line segment that connects the center point to any point on the circle **All radii of a circle are equal
chord
a chord is a line segment that connects two points on a circle
diameter
a diameter is a chord that contains the center point
tangent
a tangent is a line that intersects a circle at exactly one point
semicircle
a semicircle is half of a circle
minor arc
a minor arc is a part of a circle that is less than 180°
major arc
a major arc is a part of a circle that is more than 180°
central angle
a central angle is an angle whose vertex is the center of the circle
reflex angle
a reflex angle is an angle whose measure is more than 180°
degree measure of an arc
the degree measure of an arc is equal to the measure of its central angle
inscribed angle
an inscribed angle is an angle whose vertex is on the circle and whose two sides intersect the circle at two other points
secant angle
a secant angle is an angle whose two sides intersect the circle at at least two different points and whose vertex is not on the circle
Chord and Diameter Theorem 56:
Chord and Diameter Theorem 56: Iff a line through the center of the circle is perpendicular to a chord, then it also bisects the chord.
Tangent and Radius Theorem 59:
Tangent and Radius Theorem 59: iff a line is tangent to a circle, it is perpendicular to the radius drawn to the point of contact
Equal Chords Theorem 61:
Equal Chords Theorem 61: Equal Chords have equal arcs
Inscribed Angles Theorem 63:
Inscribed Angles Theorem 63: An inscribed angle is equal to half its intercepted arc
Inscribed Angles of a Semi-Circle Corollary:
Inscribed Angles of a Semi-Circle Corollary: The inscribed angle of a semi-circle is 90°
Secant with Inside Vertex Theorem 64:
A secant angle whose vertex is inside the circle is equal to half the sum of its intercepted arcs
Secant with Exterior Vertex Theorem 65:
A secant angle whose vertex is outside the circle is equal to half the difference of its two intercepted arcs
Two Tangents from an External Point Theorem 66:
Two Tangents from an External Point Theorem 66: The tangent segments to a circle from an external point are equal
Two Intersecting Chords Theorem 67:
If two chords intersect in a circle, the product of the length of their intersected segment parts is equal.
slope-intercept form of a line
y = mx + b (m is the slope, b is the y-intercept)
point-slope form of a line
(y-y₁) = m(x-x₁)
