Chapter 10.1 - 10.3 Circles Flashcards
Exterior of a circle
Points outside of a circle.
Chord
A segment whose endpoints are on the circle.
Diameter
A chord that passes through the center of a circle.
Radius
A segment whose endpoints consist of the center of the circle and a point on the circle.
Tangent
If a line intersects a circle at exactly one point, then the line is a tangent of the circle.
Secant
If a line intersects a circle at two points, then the line is a secant of the circle.
Common tangent
A line that is tangent to two circles.
Common external tangent
A common tangent that does not intersects the segment that joins the centers of the circle.
Interior of a circle
Points inside of a circle.
Common internal tangent
A common tangent that intersects the segment that joins the centers of the circle.
Two circles can intersect in 4 different ways:
1) two circles can have no points of intersection.
2) two circle can have exactly one point of intersection ( circles are tangent to each other ).
3) two circles can have exactly two points of intersection.
4) two circles can have infinitely many points of intersection.
Concentric circles
Circles that have the same center.
Congruent circles
Circles with congruent radii or diameters.
Theorem 10.1
If a line is tangent to a circle, then it is perpendicular to the radius drown to the point of tangency.
Theorem 10.2
In a plane, if a line is perpendicular to a radius of a circle, at its endpoints on the circle, then the line is tangent to a circle.
Theorem 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 the polygon is tangent to the circle.
Circumscribed circle
A circle is circumscribed about a polygon if each vertex of a polygon lies on the circle.
Circle
Set of all points in a plane that are equidistant from a given point called the center.
Central Angle
An angle whose vertex is the center of the circle.
Minor arc
Consists of the endpoints of the central angle and all points on the circle that are in the interior of the central angle.
Measure of a minor arc
The measure of the central angle.
Semicircle
An arc whose endpoints arc the endpoints of the diameter.
Major arc
Consists of the endpoints of the central angle and all points on the circle that lie in the exterior of the central angle.
Adjacent arcs
Two arcs of the same circle are adjacent if they intersect at exactly one point.
Postulate 21 Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Congruent arcs
In the same circle or congruent circles, two arcs are congruent if they have the same measure.
Theorem 10.4
In the same circle or in congruent circles, two arcs are congruent iff their central angles are congruent.
