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GEOMETRY Properties of Circles
Name _______________________________
Notes 8-0, Properties of Circles
Date _________________ Period _________
Properties of Circles
Directions: For each section, use the indicated GeoGebra applet, along with the Word Bank,
to fill in the blanks below.
endpoints
vertex
perpendicular
equidistant
chords
greater than
Word Bank (you will use some words more than once)
central
bisects
congruent
one
arc
one
right
supplementary
less than
equal to
not
8-1 Circles
A ____________ angle is an angle with its vertex on the center of a circle.
Use the GG-ArcMeasure applet to complete this property about arc measure:
The measure of an arc of a circle is equal to the measure of its ____________ angle.
The measure of a minor arc is ________________ 180o.
The measure of a major arc is ________________ 180o.
The measure of a semicircle is _______________ 180o.
Arc Length is ________ the same as arc measure.
Arc Length =
or
Arc Length =
8-2 Arcs and Chords – The arc of a chord is a minor arc that shares the _________________ of a chord.
Use the three GeoGebra applets in section 8-2 to complete these conjectures:
Circle Conjecture #1: If two chords in a circle are congruent, then their arcs are _______________.
Circle Conjecture #2: If a radius (or diameter) of a circle is perpendicular to a chord,
then it ___________ the chord and its arc.
Circle Conjecture #3: If two chords in a circle are congruent, then they are ___________________
from the center.
8-3 Inscribed Angles – An inscribed angle is an angle whose ______________ is on a circle,
and whose sides are ______________ of the circle.
Use the four GeoGebra applets in section 8-3 to complete these conjectures:
Circle Conjecture #4: If an angle is inscribed in a circle, then the measure of the angle is equal to
one-half the measure of its intercepted _________.
Circle Conjecture #5: If two inscribed angles of a circle intercept the same arc, then
the inscribed angles are __________________.
Circle Conjecture #6: If an inscribed angle of a circle intercepts a semicircle, then the
inscribed angle is a ______________ angle.
Circle Conjecture #7: If a quadrilateral is inscribed in a circle, then its opposite angles
are ___________________.
8-4 Tangents
A tangent is a line that intersects (touches) a circle at
exactly ________ point.
Draw a picture of a circle with a tangent line in the box to the right.
Label the point of tangency Q.
Use the four GeoGebra applets in section 8-4 to complete
these conjectures:
Circle Conjecture #8: If a line is tangent to a circle, then the line is ________________________ to
the radius drawn to the point of tangency.
Circle Conjecture #9: If two segments from the same external point are tangent to a circle,
then the segments are ____________________.
8-5 Inside and Outside Angles
Use the two GeoGebra applets in section 8-5 to come up with these two formulas:
Circle Conjecture #10: If an angle is formed by two chords intersecting inside a circle,
then the measure of the angle is
m(Inside Angle) =
Circle Conjecture #11: If an angle is formed by two secants (or tangents) intersecting outside a circle,
then the measure of the angle is
m(Outside Angle) =