Geometry A Unit 10 Day 1 Warm-Up
Circles: Vocabulary and Basic Theorems
I. Before we start: A circle is all of the points that are a certain distance from a given
point (its center). The circle to the right would be called  T.
It is important to know that, even though circles are named
for their centers, the only points ON the circle are those
one radius away from the center. So points T and S are
not on the circle, only M is.
diagram A
S
T
I. Segments in Circles –
1. Radius – A segment that goes from the center of a circle to a point on
the circle.
M
diagram B
2. Diameter – A segment that passes through the
center of the circle, connecting two
points on the circle.
B
A
B. Ones we might not know –
1. Chord – Any segment that connects two points.
on a circle.
2. Secant – A LINE that passes through two points
on a circle.
C
E
D
3. Tangent – A line or segment that touches a circle at exactly one point.
4. Point of tangency – The point where a tangent intersects a circle.
Use the definitions above to match the term with the correct line, point or segment. (Use
diagram B)
1. Radius ______
a. FG
2. Diameter _____
b. DE
3. Chord ______
c. CB
4. Secant ______
d. D
5. Tangent ______
e. BD
6. Point of Tangency ______
f. AB
G
F
C. Theorems about segments and lines on circles.
1. In the diagram, a tangent and a radius intersect. Name the tangent ____
and the radius _______.
2. Theorem – A radius and an tangent drawn on the same triangle cross at 90o.
3. Find the length of the radius.
41
D
F
40
Radius of Circle D measures __________
E
4. In the diagram below, SR and ST are two tangents to the same circle
that cross at point S.
5. Theorem: The distances from a point outside a circle to two points of tangency are =.
S
6. Solve for x in the diagram to the right.
2x2 + 2
R
x = __________
20
T
Arcs and Chords
A. Arc – A curved portion of a circle
1. Minor Arc – an arc that measures less than 180o.
a. Use two letters and this symbol to name one.
T
Ex: _____
2. Major Arc – an arc that measures more than 180o.
a. Use 3 letters and arc symbol.
Ex: _______
3. Semicircle – an arc that measures exactly 180o.
a. They can be indicated by a diameter. Ex: _______
M
V