Chapter 10 ­ Circles
10.1 ­ Tangents to Circles
Key Terms:
Circle
Center
Radius
Diameter
Chord
Secant
Tangent
Concentric
Common Tangent
Interior / Exterior
Point of Tangency
Mar 1­7:13 AM
A CIRCLE is the set of all points in a plane equidistant from a given point called the CENTER. A circle with center P is called "circle P" or P.
P
Mar 1­7:22 AM
Radius, Chord, Diameter
R
The RADIUS is a segment whose endpoints are the center and a point on the circle. QP, QR and QS are all radii of Q.
Q
S
A CHORD is a segment whose endpoints are on the circle. PS and PR are chords of Q.
P
A DIAMETER is a chord that passes through the center of a circle. PR is a diameter of Q. The diameter is the longest possible chord of a circle.
Mar 1­7:29 AM
1
A TANGENT is a line coplanar to the circle that intersects the circle in 1 place.
A SECANT is a line that intersects a circle in 2 points.
j ­ Tangent
j
k
k ­ Secant
Mar 1­7:32 AM
Example 1: Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter or a radius of C
K
a.) AD
B
b.) EG
c.) CD
A
J
C
H
D
d.) HB
G
F
E
e.) GK
Mar 1­11:18 AM
CONCENTRIC CIRCLES ­ Non­intersecting circles that have the same center point.
X
Mar 2­7:46 AM
2
In a plane, two circles can intersect in two points, one point or no points.
Coplanar circles that intersect in one point are called TANGENT CIRCLES.
Internally Tangent
Externally Tangent
Mar 2­7:41 AM
COMMON TANGENT­ A line or segment that is tangent to two coplanar circles.
A COMMON INTERNAL TANGENT intersects the segment joining the center of the two circles. A COMMON EXTERNAL TANGENT does not intersect the segment joining the center of the two circles. Mar 3­7:13 AM
Theorem 10.1 ­ If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Q
Radius
t
R
Tangent Line
@ R
Mar 3­7:17 AM
3
Line t is tangent to Circle Q at Point R. How can we solve for QP?
Q
10
t
24
R
P
Mar 3­7:17 AM
Q
62
11
R
t
60
t
Is line a tangent line to circle Q? Verify your answer.
Mar 3­7:22 AM
Finding the Radius of a Circle.
r
r
18
24
Mar 3­7:24 AM
4
We have used tangents to circles since the birth of Astronomy. For example:
With a telescope, we locate the moon of a planet. We are able to tell that the moon is orbiting the planet 170,000 miles away. Figuring that the moon is 250,000 miles away from the horizon, we are able to tell how big this new planet is. What is the diameter of the planet?
Feb 28­8:25 AM
*Tangent segments from a common external point are congruent.
r
r
Feb 28­6:49 AM
Solve for x.
­2x + 27
C
D
A
3x ­ 8
B
Feb 28­6:49 AM
5