Tangents to circles

1. Lesson 6.1 Tangents to Circles
Goal 1 Communicating About Circles
Goal 2 Using Properties of Tangents

2. Communicating About Circles
Circle Terminology:
A CIRCLE is the set of all points in the plane
that are a given distance from a given point. The
given point is called the CENTER of the circle.
A
A circle is named
by its center point.
“Circle A”
or A

3. Communicating About Circles
Radius
Chord
Diameter
Tangent
Secant
Parts of a Circle
Point of Tangency

4. Communicating About Circles
A C
A
C
A
C
In a plane, two circles can intersect in two
points, one point, or no points.
Two Points
One Point
No Point
Coplanar Circles
that intersect in one
point are called
Tangent Circles

5. Communicating About Circles
Tangent Circles
A line tangent to two coplanar circles is
called a Common Tangent

6. Communicating About Circles
Concentric Circles
Two or more coplanar circles that share the same center.

7. Communicating About Circles
Common
Internal
Tangents
Common
External
Tangents
Common External Tangent
does not intersect the
segment joining the centers
of the two circles.
Common Internal Tangent
intersects the segment
joining the centers of the
two circles.

8. Communicating About Circles
A circle divides a plane into three parts
1.Interior
2.Exterior
3.On the circle

9. Using Properties of Tangents
If a line is tangent to a circle, then it is perpendicular to
the radius drawn to the point of tangency.
Radius to a Tangent Conjecture
The Converse then states:
In a plane, if a line is
perpendicular to a radius of a
circle at the endpoint on the
circle, then the line is a tangent of
the circle.

10. Using Properties of Tangents
45
43
11
R
S
T
Is TS tangent to R? Explain
If the Pythagorean
Theorem works then the
triangle is a right
triangle  TS is tangent
222
114345 
?
12118492025 
?
19702025 NO!

11. Using Properties of Tangents
You are standing 14 feet from a water tower. The
distance from you to a point of tangency on the
tower is 28 feet. What is the radius of the water
tower?
r
14 ft
28 ft
r
R
S
T
Radius = 21 feet Tower
  222
2814 rr 
222
2819628 rrr 
78419628 r
58828 r
21r

12. Using Properties of Tangents
If two segments from the same exterior
point are tangent to the circle, then they
are congruent.
Tangent Segments Conjecture
ACAB 

13. Using Properties of Tangents
21
R
S
U
V
x2 - 4US is tangent to R at S.
is tangent to
R at V.
Find the value of x.
UV
2142
x
252
x
5x

14. Using Properties of Tangents
x
z 15
y36
R
S
U
V
Find the values
of x, y, and z.
All radii are =
y = 15
222
1536 x
22512962
x
15212
x
39x
Tangent segments are =
z = 36