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47 Cards in this Set

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circle
the set of all points in a plane that are equidistant from a given point, called the center
radius
the distance from the center to a point on the circle is the radius of the circle
congruent
two circle are congruent if they have the same radius
diameter
the distance across the circle, through its center of the circle and a point on the circle
chord
a chord is a segment whose endpoints are points on the circle
diameter
a diameter is a chod that passes through the center of the circle
secant
a secant is a like that intersects a circle in two points
tangent
a tangent is a line in the plane of a circle that intersects the cicle in exactly one point
Theorem 10.1
If a line is tangent ot a circle, then it is perpendicular to the radius drawn to the point of tangency
Theorem 10.2
In a plane, if a line is perpendicular to a radius of a cicle at its endpoint on a circle, then the line is tangent to the circle
Theorem 10.3
If two segments from the same exterior point are tangent to a circle then they are congruent
tangent circle
coplanar circles that intersect in one point
concentric
coplanar circles that have a common center
common tangent
a line or segment that is tangent to two coplaner circles
interior of a circle
consists of th epoints that are inside of the circle
exterior of a circle
consists of the points that are outside the circle
point of tangency
the point at which a tangent line intersects the circle to which it is tangent
central angle
an angle whose vertex is the center of a circle
minor arc
the arc that is made when a circle that is divided by an angle is less than 180 degrees
major arc
the larger arc that is made when a circle is divded by an angle
semicircle
when the endpoints of an arc are the endpoints of a diameter
measure of a minor arc
the measure of central angle when a circle is cut by an angle
measure of a major arc
the differnt betweo 360 degrees and the measure of its associated minor arc
Postulate 26- Arc Addition Postulate
The measure of an arc fromed by two adjacent arcs is the sum of the measures of the two arc
congruent arcs
two arcs of the same circle of of congruent circle that have the same measure
Theorem 10.4
In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding corgs are congruent
Theorem 10.5
If a diameter of a circle is perpendicular to a chord, then the diameter biscets the chord and its arc
Theorem 10.6
If one chord is a perpendicular bisector of another chord then the first chord is a diameter
Theorem 10.7
In the same circle, or in congruent circles, two cords are congruent if and only if they are equidistant from the center
Inscribed angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
Intercepted arc
the arc that lies in the interiorof an inscribed angle and has the endpoints on the angle
Theorem 10.9
If two inscribed angle of a cicle intercept at the same arc then the angles are congruent
inscribed
If all the vertices of a polygon lie on a circle the polygon is inscribed in the circle and the circle is circumscribed
circumscribed
If all the vertices of a polygon lie on a circle the polygon is inscribed in the circle and the circle is circumscribed
Theorem 10.10
If a right triangle is inscribed in a circle then the hypotenus is a diamter of the circle. Conversely,if one side of an inscribed triangle is a diameter of the circle, then the tirangle is a right triangle and the angle opposite the diameter is the right angle
Theorem 10.11
A quadrilateral can be inscribed in a circle if an donly if its opposite angles are supplementary
Theorem 10.12
If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is one half the measure of its intercepted arc
Theorem 10.13
If two cords intersect in the interior of a circle then the measure of each angle is one half the sum of the measure of the arcs interpected by the angle and its vertical angle
Theorem 10.14
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle then the measure of the angle formed is one half the difference of the measure of the intercepted arcs
Theorem 10.15
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lenghts of the segments of the other chord
tangent segment
a segment of a tangent that is before hitting the point of tangency
secant segment
a segment of a secant
external secant segment
the outside section of a secant that has yet to intersect with the circle
Theorem 10.16
If two secant segments share the same endpoint outside of a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment
Theorem 10.17
If a secant segment and a tangent segment share and endpoint outside a circle, the the product of the lenth of the secant segment and the length of its external segment equals the square of the length of the tangent segment
Standard equation of a circle
using the distance formula to find the radius of a circle on a coordinate plan using the center of the circle and an outside point
Locus
the set of all points in a plane that satisfy a fiven condition or a set of given conditions