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Honors Geometry
Chapter 10
Name
Section 10.1
What is a circle?
What is the center of a circle?
What is the radius of a circle?
What is plural for radius?
What are concentric circles?
In order for circles to be congruent, they must have
.
A point is in the interior of a circle, if its distance from the center is
the radius.
A point is in the exterior of a circle, if its distance from the center is
the radius.
A point is on the circle if its distance from the center is
the radius.
What is a chord?
What is the longest chord?
What is a diameter?
How do you find the area of a circle?
How do you find the circumference of a circle?
The distance from the center of a circle to a chord is
.
If a radius is perpendicular to a chord, then
.
If a radius of a circle bisects a chord that is not a diameter, then
.
The perpendicular bisector of a chord passes through
.
Section 10.2
If two chords of a circle are equidistant form the center, then
.
If two chords of a circle are congruent, then
.
Answer the question following the proof in Sample Problem 2 on page 447.
Section 10.3
What is an arc?
What is the center of an arc?
What is a central angle?
What is a minor arc?
What is a major arc?
What is a semicircle?
What is different about naming a major arc versus a minor arc?
The measure of a minor arc = measure of the
angle.
A minor arc measures how many degrees?
A semicircle measures how many degrees?
A major arc measures how many degrees?
Two arcs are congruent when they
1.
2.
In the same circle or in congruent circles,
Section 10.4
What’s a secant line of a circle?
What’s a tangent line of a circle?
The place where a tangent line intersects a circle is called
.
What’s the relationship between a tangent line and the radius drawn to the
point of contact?
What’s a tangent segment of a circle?
What’s a secant segment of a circle?
In your own words what’s the external part of a secant segment?
Two-Tangent Theorem
If two tangent segments are drawn to a circle from an external point,
then
What are tangent circles?
.
When are two circles externally tangent?
When are two circles internally tangent?
Two tangent circles intersect on what line?
What is a common tangent?
What is a common internal tangent?
What is a common external tangent?
How many common tangents do two externally tangent circles have?
How many common tangents do two internally tangent circles have?
How many common tangents do two non-intersection circles have?
How many common tangents do two intersecting circles have? (Intersecting
circles intersect at more than one point.)
How many common tangents do two concentric circles have?
What are the five steps in the Common-Tangent Procedure?
1.
2.
3.
4.
5.
Section 10.5
What two kinds of angles have vertices on the circle? Describe each angle.
1.
2.
The measure of an angle whose vertex is on a circle =
.
What kind of angle has it’s vertex in a circle but not at the center?
Describe this angle.
The measure of an angle whose vertex is in a circle but not at the center =
.
What three kinds of angles have their vertices outside of a circle?
Describe each angle.
1.
2.
3.
The measure of an angle whose vertex is outside a circle =
.
Section 10.6
2 inscribed or tangent-chord angles intercept the same arc (or congruent
arcs)
An angle inscribed in a semicircle is a
angle.
Measure of a tangent-tangent angle + measure of its minor arc =
Section 10.7
What does it mean for a polygon to be inscribed in a circle?
What does it mean for a polygon to be circumscribed about a circle?
What’s a circumcenter?
What’s an incenter?
Quadrilateral inscribed in a circle
opposite angles are
Parallelogram inscribed in a circle
Diagonals of a parallelogram inscribed in a circle are also
of the circle.
The diagonals of a parallelogram inscribed in a circle intersect at the
of the circle.
Section 10.8
Chord-Chord Power Theorem
Tangent-Secant Power Theorem
A
A
B
E
B
C
D
C
D
=
=
Secant-Secant Power Theorem
A
B
C
D
=
Section 10.9
The circumference is the
of the circle.
What’s the formula for the circumference of a circle.
How do you find the length of an arc?