Circles Unit
Geometry 2
Vista Grande High School
2/21/2011
NO SCHOOL
2/28/2011
Inscribed Angles 10.3
Worksheet Page 8
Other Angle Relationships in
Circles 10.4
Pg. 624: 8 - 28
3/7/2011
Equations of Circles 10.6
Page 638: 13-25
2/22/2011
Tangents to Circles 10.1
Vocabulary
Pg 599: 9 – 25; 36, 37,46,47
Arcs & Chords 10.2
Worksheet Page 7
3/1/2011 - AIMS Wtg
3/8 AIMS Wtg M/U
Equations of Circles 10.6
Page 638: 13-25
2/23/2011
Tangents to Circles 10.1
Vocabulary
Pg 599: 9 – 25; 36, 37,46,47
Arcs & Chords 10.2
Worksheet Page 7
3/2/2011 AIMS Rdg
3/9 AIMS Rdg M/U
Circle Review
Chapter Rvw WS Pg. 12/13
2/24/2011
2/25/2011
Work on Topographical
Trails Project
Work on Topographical
Trails Project
3/3/2011
Inscribed Angles 10.3
Worksheet Page 8
Other Angle Relationships in
Circles 10.4
Pg. 624: 8-28
3/10/2011
Circle Review
Chapter Rvw WS Pg. 12/13
3/4/2011
Segment Lengths in Circles
10.5
Worksheets Pgs. 9, 10, & 11
3/11/2010 Qtr 3 Ends
Circle Test (Chapter 10)
-------------------S P R I N G
B R E A K-------------------Materials available at spartansmath.wikispaces.com or spartansmathdolezal.wikispaces.com
Math Help Available: Black Lunch – Room 1218 (Ms. Wildermuth) or Gold Lunch – Room 1215 (Mrs. Hodge)
Book located at: http://www.nexuslearning.net/books/ML-Geometry/
Term
Definition (in words)
Example (visual)
Circle
Set of all points in a plane that are
_____________ from a given point.
Diameter
Distance across the circle through its
___________.
Radius
Segment whose endpoints are the _________
of the circle and a point on the circle.
Tangent
A line in a plane that intersects the circle in
exactly ___ _______________.
Center
The point from which all points of a _________
are equidistant from.
Chord
A segment whose endpoints are points
______ the circle.
Secant
Line that intersects a circle in ______ points.
Label each term on the drawing below.
1
Arcs, Chords, Angles, and Segments
Main Idea
Details
Examples
* * * * * * * * * * * * * * TERMS * * * * * * * * * * * * * *
Draw a circle with radius 12. Then
draw radii OA and OB to form a 60
Circle – the set of points in a ___________ at a given distance from the given
degree angle. Find the length of AB.
point in that plane.
Center - the given point for the set of points equidistant from it.
Radius – Any ____________ that joins the ____________ to a point of the
circle. It is ____ the diameter.
Chord – a ______________ whose endpoints lie _______ the circle.
If a circle has a diameter of 24,
Secant – a line that contains a ____________.
then it has a radius of ______.
Diameter – a ____________ that contains the __________ of a circle. It is
____ the radius.
If a circle has a radius of 15, then it
has a diameter of _______.
Tangent – a _________ in the plane of a circle that intersects the circle in exactly
___ ___________.
If a circle has a radius of 8, then it
Point of Tangency – the one ___________ that a tangent intersects a circle.
has a diameter of ______.
Common Exterior Tangent – intersect at a point _________________________.
If a circle has a diameter of 7, then
Common Interior Tangent – do not _________________________.
it has a radius of ______.
Sphere – The set of all points in ________ at a given distance from a given point.
The segment that joins the centers
of two circles is intersected by a
Congruent Circles (or spheres) – circles (or
common ______ tangent, if there is
spheres that have congruent
______________.
one.
Concentric circles – circle that lie in the
A line which intersects a circle at
same _________________ and have the
exactly one point is called
same ________.
________.
If a line is ___________ to a circle, then the
line is __________________ to the radius
Theorem about
B
drawn to the point of tangency.
Tangents and
Radii
What is true about BAD to the right?
A
B
O
B
13
D
B
12
BA
B
You are standing at Point B
B
BB10 feet from the center of
B the circular water storage
tank and 7 feet from the
B
Point A. AB is tangent to
the circle. Find the radius
of the tank.
2
Theorem about
Tangents from
the Same Point
Tangents to a circle from a point are
2x + 3
_______________.
6x - 5
Theorem about
a Chord and a
Radius
Perpendicular
A radius that is perpendicular to a chord
____________ the chord.
Find the radius of the
circles.
to the Chord
Arc – an unbroken part of the circle. Two
endpoints are always the endpoints of two arcs.
Minor Arc – less than ____________. Use __
letters to name a minor arc.
Arcs
Semicircle – the two endpoints are the
endpoints of a _________________.
Major Arc - greater than __________. Use
___ letters to name a major arc.
An angle of a circle with its vertex at the
__________ of the circle.
Central Angle
A full circle is ____ .
The measure of a central angle’s intercepted arc is
_______ to measure of the central angle.
3
How many degrees does a minute hand move
in…
5 minutes?
30 minutes?
15 minutes?
45 minutes?
20 minutes?
10 minutes?
Definition:
Draw an inscribed angle that intercepts a minor
arc.
Inscribed Angle
Draw an inscribed angle that intercepts a major arc.
The measure of an inscribed angle is equal to
Measurement of
an Inscribed
Angle
______________ the measure of its
____________________ arc.
If two inscribed angles intercept the same
arc, then the angles are
_______________.
Corollaries
An angle inscribed in a semicircle is a
____________________ angle.
If a quadrilateral is inscribed in a circle,
then its opposite angles are
__________________________.
4
The measure of an angle formed by a chord
and a tangent is equal to ____________
the measure of the intercepted
Angles formed
____________.
by Chords and
Tangents
The measure of an angle formed by two
chords that intersect inside a circle is equal
Other Angles
to ______________ te
_______________ of the measures of the
Measures of
intercepted arcs.
angles formed
by two chords
inside a circle
The measure of an angle formed by two
secants, two tangents, or a secant and a
tangent drawn from a point outside a circle
Measure of
angles formed
segments that
is equal to _____________ the
_________________ of the measure of
the intercepted arcs.
intersect
outside the
circle.
5
Segment of a chord is used to refer to the
Segments of
a Chord
length of a segment as well as to the
segment itself.
When two chords intersect inside a circle,
Lengths of
chords
intersecting
inside the
circle
the __________________ of the
segments of one chord equals the
___________________ if the segments of
the other chord.
When two secant segments are drawn to a
circle from an external point, the
_________ of one secant segment and its
Lengths of
segments that
intersect
outside the
circle
external segment equals the ____________
of he other secant segment and its external
segment.
When a secant segment and a tangent are
drawn to a circle from an external point, the
__________________ of the secant
segment and its external segment is equal to
the ____________ of the tangent segment.
6
7
8
9
10
11
12
13