MIDTERM Flashcards
(30 cards)
Cosecant
1/sin
Secant
1/cos
Arc Addition Postulatr
Measure of two adjacent arcs is equal to the sum of the measure of the two arcs
Inscribed Angle Theorem
Measure of an inscribed angle is one half measure of its intercepted arc
Parallel Lines Congruent Arcs Theorem
Parallel lines intercept congruent arcs on a circle
Interior Angles of a Circle Theorem
“If an angle is formed by two intersecting
chords or secants such that the vertex of the angle is in the interior of the circle, then the
measure of the angle is half the sum of the measures of the arcs intercepted by the angle
and its vertical angle.”
Exterior Angles of a Circle Theorem
“If an angle is formed by two intersecting
secants, two intersecting tangents, or an intersecting tangent and secant such that the
vertex of the angle is in the exterior of the circle, then the measure of the angle is half the
difference of the measures of the arc(s) intercepted by the angle
Tangent to a Circle Theorem
A line drawn tangent to a circle is perpendicular to
a radius of the circle drawn to the point of tangency
Diameter-Chord Theorem
If a circle’s diameter is perpendicular to a chord, then
the diameter bisects the chord and bisects the arc determined by the chord.”
Equidistant Chord Theorem
“If two chords of the same circle or congruent circles
are congruent, then they are equidistant from the center of the circle
Congruent Chord–Congruent Arc Theorem
“If two chords of the same circle or
congruent circles are congruent, then their corresponding arcs are congruent.”
Segment-Chord Theorem
“If two chords in a circle intersect, then the product of
the lengths of the segments of one chord is equal to the product of the lengths of the
segments of the second chord.
Tangent Segment Theorem
“If two tangent segments are drawn from the same
point on the exterior of a circle, then the tangent segments are congruent
Secant Segment Theorem
“If two secant segments intersect in the exterior of a
circle, then the product of the lengths of one secant segment and its external secant
segment is equal to the product of the lengths of the second secant segment and its
external secant segment.”
IMPORTANT
Secant Tangent Theorem
“If a tangent and a secant intersect in the exterior of a
circle, then the product of the lengths of the secant segment and its external secant
segment is equal to the square of the length of the tangent segment.”
Inscribed Right Triangle–Diameter Theorem
If a triangle is inscribed in a
circle such that one side of the triangle is a diameter of the circle, then the triangle is a
right triangle
Inscribed Quadrilateral–Opposite Angles Theorem
“If a quadrilateral is inscribed
in a circle, then the opposite angles are supplementary.”
Arc Length
s = degree of seg arc/360 x 2(pi)r
Radian
Arc Length = radius length (s/r)
Area of sector
a = degree of sec/360 x (pi)r^2
Volume of cylinder
(pi)r^2 x h
Volume of Cone
1/3(pi)r^2 x h
Sphere
4/3(pi)r^3
standard form of the equation of circle
(x-h)^2 + (y-k)^2 = r^2
