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50 Cards in this Set

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  • Back
chords
segment that goes from endpoint to endpoint on a circle
The central angle is equal to 1/2 of the
intercepted arc
Inscribed angless are formed by
two chords with a common endpoint on the circle
tangent
a line that touches one point on the circle
The measure of an angle formed by a tangent and a chord is equal to half of its
intercepted arc
The measure of an inscribed angle is equal to half of its
intercepted arc
tangent
touches one part of the circle
Point on the circle
A point on the outer rim of the circle
chords
still touches two points of the circle
chord
is also called a segment
secant
a line that keeps going through the circle at two points
a secant
is a line that contains a chord
Diameter
cuts the circle into 2 semi-circles
Diameter
two times the radius and it goes through the center. The length of the diameter is the longest chord
minor arc
smaller than a semicircle. It is named using only its two endpoins. Is measure is equal to the measure of its central angle
The endpoints of a semicircle are the endpoints of a ________ of the circle.
diameter
A tangent line is a line that intersects a circle in exactly one point called the
point of tangency
A Central angle is equal to its
intercepted arc
semi-circle
180 degrees is the measure for each half
Theorem #1 The measure of a Central Angle is equal to its
intercepted arc
Theorem #2 The measure of the inscribed angle equals _____ of its intercepted arc
half (on page 5)
Theorem # 3 The measure of an angle formed by a tangent and a chord with its vertex on the circle is equal to half of its
intercepted arc
If a right angle is inscribed in a circle, then the hypotenuse is a _______ of a circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
diameter
If two inscribed angles of a circle intercept the same arc, then the angles are ________.
congruent
sin
opposite/hypoteneuse
Theorem 8
A quadrilateral can be inscribed in a circle if and only if its opposite angles are
supplementary
opposite angles need to be________ if they are inscribed in a circle
supplementary
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its ____________ angle
vertical
The sum of a linear pair equal
180 degrees
Your quiz is on
Wednesday
Theorem 11
If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the ____________ arcs.
intercepted
When subtracting the two arcs start with the
larger
Linear equation because our highest power is
one
Quadratic equation: the largest power is
2
Intercepted arcs are the arcs
within the angle that it forms
Theorem 16
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is ______ to the product of the lengths of the segments of the other chord
equal
Theorem 17
If two secant segments share the same endpoint outside a circle, then the _______ of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its _______ segment.
product
external
secant segment
a segment that contains a chord of a circle and has exactly one endpoint outside of the circle
a secant that contains a chord of a circle and has exactly one endpoint outside of the circle
secant segment
external segment
the part of the secan segment that is outside of the circle
Theorem 6
If a right angle is inscribed in a circle, then the ___________
is a diameter of a circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then triangle is a
____________ triangle and the angle opposite the diameter is the right angle
hypotenuse
right
Sin = opposite/
HYPOTENUSE
Theorem 7
If two inscribed angles of a circle intercept the same ____, then the angles are congruent.
arc
Theorem 8
A quadrilateral can be inscribed in a circle if and only if its opposite angles are ______________
supplementary
Vertical angles are ________
congruent
Theorem 10
If 2 chords intersect inside a circle, the measure of each angle is one half the sume of the _______ of the arcs intercepted by the angle and its vertical angle.
measures
The measure of 2 angles in a ______pair is 180 degrees.
linear
Great Circle
Circle that divides a sphere into 2 semi-spheres. Like the equator, it breaks up the Earth into two halves.
Circle =26 inches
2∏r=26
r=26/(2∏)=4.14

r=4.14 inches
Surface Area
two dimensional