Chapter 10 Flashcards
Chord
A segment whose endpoints are on a circle
Cirle
Set of. All points in a plane that are equidistant from a certain point called the center. The points inside the circle form it’s interior. The points outside the circle form it’s exterior.
Diameter
A chord that passes through the center
Radious
A segment that has a center as one endpoint and a point on the circle as another
Tangent
A line that intersects a circle at exactly one point
Point of tangency
The point at which the tangent intersects
Secant
A line that intersects a circle at two points
Common tangent
A line that is tangent to two circles
Common external tangent
A common tangent that does not intersect the segment that joins the centers of the circles
Common internal tangent
A common tangent that intersects the segment that joins the centers of the circles
Concentric circles
Circles that have the same center
Congruent circles
Circles with congruent radii or diameters
Thm 10.1
If a line is tangent to a circle then it is perpendicular to the radio us drawn to the point of tangency
Thm 10.2
In a plane, if a line is perpendicular to a radius of a circle at its endpoints on a circle then the line is tangent to the circle
Thm 10.3
If two segments from the same exterior point are tangent to a circle, then they are congruent
Inscribed circle
A circle is inscribed in a polygon if each side of a polygon is tangent to a circle
Circumscribed circle
A circle is circumscribed about a polygon if each vertex of the polygon lies on the circle
Central angle
An angle whose vertex is the center of a circle and whose sides pass through a pair of points on the circle
Minor arcs
A shorter ace joining two points together on a circumference
Measure of a minor arc
The smaller arc when a circle is divided unequally
Semi circle
A circle cut on the diameter
Major arc
A longer arc joining two points together on a circumference
Measure of a major arc
The bigger arc when a circle is divided unequally
Adjacent arc
Two arcs on a circle that share exactly one endpoint
Arc addition postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures in the arcs
Congruent arcs
Arcs with the same measure on the same congruent circles
Thm 10.4
In the same circles, or in congruent circles, two arcs are congruent iff their central angles are congruent
Thm 10.13
If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is half the measure of the intercepted arc
Thm 10.14
If two chords intersect in the interior of a circle, then the measure of each angle is half the sum of the measures of the arcs intercepted by the angle, and it’s verticals angle
Thm 10.15
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 half the difference of the measures of the intercepted arcs
Thm 10.5
In the same circle or in congruent circles, two minor arcs are congruent iff their corresponding chords are congruent
Thm 10.6
If a diameter of a circle is perpendicular to a chord, then the diameter bisects it’s chord at the arc
Thm 10.7
If a chord is perp to a bisector of another chord, then it is the diameter
Thm 10.8
In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center
Inscribed angle of a circle
An angle who’s vertex is on the circle and sides are part of the circle
Intercepted arc
Te arc that lies in the interior of an inscribed angle
Thm 10.9
If an angle is inscribed in a circle then it’s measure is half the measure of it’s intercepted arc
Thm 10.10
If two inscribed angles of a circle intercept the same arc, then the angles are congruent
Thm 10.11
An angle that is inscribed in a circle is a right angle iff it’s corresponding arc is a semicircle
Thm 10.12
A quadrilateral can be inscribed in a circle iff it’s opposite angles are supplementary
