Chapter 12: Circles Flashcards
(35 cards)
Definition 60: A circle is
the set of all points in a plane that are at a given distance from a given point, called the center, in the plane.
Definition 61: A radius is
a line segment that joins the center of the circle to a point of the circle.
Postulate 17: All radii of the same circle are
congruent
Definition 62: A chord of circle is
a line segment that joins two points of the circle.
Definition 63: Diameter of a circle is
a chord that contains the center
Definition 64: A tangent line is
a line which interests a circle at exactly one point; the point of contact of called the point of tangency.
Definition 65: A secant line is
a line which interests a circle at two different points
Theorem 61: If a line through the center of a circle is perpendicular to a chord, it
also bisects the cord.
Theorem 62: In the same circle, congruent chords are equidistant (the same distance) from
the center of the circle.
Theorem 63: In the same circle, chords equidistant form the center of the circle are
congruent.
Theorem 64: If a radius is drawn to the point of tangency of a tangent line, then
the radius is perpendicular to the tangent line.
Theorem 65: If a radius is perpendicular to a line at the point where the line intersects a circle, then
the line is a tangent line.
Definition 66: A tangent segment is
a line segment that has a point on the tangent line and the point of tangency as an end point.
Theorem 66: If two tangent segments are drawn to a circle from the same exterior point, then
they are congruent.
Definition 67: An arc is
a portion of a circle consisting of two end points and the set of points on the circle that lie between those points.
Definition 68: A central angle is
an angle whose vertex is at the center of the circle.
Definition 69: The degree measure of a minor arc is the
measure of its central angle.
Definition 70: The circumference of a circle is the
distance around the circle, expressed in linear units of measurement (inches, centimeters, etc.).
Theorem 67: Arc Length-Degree Measure Proportion:
Arc Length/Circumference = Degree Measure/360
Postulate 18: Arc Addition Postulate: If P is on AB, then
mAP + mPB = mAB.
Definition 71: Congruent arcs are
arcs in the same or congruent circle which have the same degree measure.
Definition 72: The midpoint of an arc is the
point on the arc which divides the arc into two congruent arcs.
Theorem 68: If two chords of the same or congruent circles are congruent, then
their minor arcs are congruent.
Theorem 69: If two minor arcs of the same or congruent circles are congruent, then
their intersecting chords are congruent.
