Circles REVIEW
Name ________________________
Accelerated Math II
Circle Vocabulary
center
tangent
central angle
minor arc
inscribed angle
tangent segments
adjacent arcs
chord
secant
arcs
semicircle
intercepted arc
secant segments
Area of a Circle: ___________
diameter
radius
common tangent
common external tangent
major arc
common internal tangent
concentric circles
arc of the chord
inscribed polygon
point of tangency
external secant segments
Circumference of a Circle: ___________
Equation of a circle in h-k form: ___________________________
Circle:
Circle: (geometric definition)
A circle divides a plane into three parts: inside the circle, outside the circle, and on the
circle;
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Circles Review
Circle Definitions and Theorems
Definition of Arc Measure: The measure of a minor arc is the measure of its central
angle. The measure of a major arc is 360º minus the measure of its central angle. The
measure of a semicircle is 180º.
Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of
the measures of the two arcs. That is if Q ia a point on PR , then
mPQ  mQR  mPQR .
In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.
In a circle or in congruent circles, two minor arcs are congruent iff their corresponding
chords are congruent.
In a circle or in congruent circles, two chords are congruent iff they are equidistant from
the center.
If an angle is inscribed in a circle, then the measure of the angle equals one-half the
measure of its intercepted arc.
If two inscribed angles in a circle (or in congruent circles) intercept congruent arcs or the
same arc, then the angles are congruent.
If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle.
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Circles Review
Acc. Math II
Name ______________________________
If a quadrilateral is inscribed in a circles, then its opposite angles are supplementary.
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of
tangency.
In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle,
then the line is a tangent of the circle.
If two segments from the same exterior point are tangent to a circle, then they are
congruent,
If s secant and a tangent intersect at the point of tangency, then the measure of each angle
formed is one-half the measure of its intercepted arc.
If two secants intersect in the interior of a circle, then the measure of an angle formed is
one-half the sum of the measures of the arcs intercepted by the angle and its vertical
angle.
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Circles Review
If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle,
then the measure of the angle formed is one-half the positive difference of the measures
of the intercepted arcs.
Case 1:
Case 2:
Case 3:
2 secants
a secant & a tangent
2 tangents
If two chords intersect in a circle, then the products of the measures of the segments of
the chords are equal.
If two secant segments are drawn to a circle from an exterior point, then the product of
the measures of one secant segment and its external secant segment is equal to the
product of the measures of the secant segment and its external secant segment.
If a tangent segment and a secant segment are drawn to a circle form an exterior point,
then the square if the measure of the tangent segment is equal to the product of the
measures of the secant segment and its external secant segment.
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