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47 Cards in this Set
 Front
 Back
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
