1. 11.1 Tangent Lines
Chapter 11 Circles

2. Tangent to a circle: a line that touches the circle at one point
Point of tangency: the point where the line and circle touch

3. Theorem 11-1:
If a line is tangent to a circle, then it is perpendicular to the radius.

4. Lines ML and MN are tangents to Circle O. Find the value of x.
What are the measures of
<OLM and <ONM?
90°
117° O
x = 360 N
x = 63°

5. ED is tangent to Circle O. Find the value of x.
38°
x = 52° O x° E D

6. A dirt bike chain fits tightly around two gears
A dirt bike chain fits tightly around two gears. The chain and gears form a figure like the one below. Find the distance between the centers of the gears. C
26.5 in E
9.3 in B D
2.4 in A
ABCE is a rectangle and AED is a right triangle.
AE is 26.5
ED is 9.3 – 2.4 = 6.9
Use Pythagorean Theorem to solve for AD.
= c2
AD = 27.4 in

7. A chain fits tightly around two circular pulleys
A chain fits tightly around two circular pulleys. Find the distance between the centers of the pulleys.
35in
14in
8in
= c2
c = 35.5in

8. If a line is perpendicular to the radius at its endpoint on the circle, then the line is tangent to the circle.
Is ML tangent to Circle N at L?
= 252 ??
= 625 ?? 25 M N
625 = 625 24 7
Yes, ML is tangent to circle N L

9. If all the vertices of a triangle are on a circle, the triangle is inscribed in the circle
When a circle is inscribed in a triangle, the triangle is circumscribed about the circle.

10. The two segments tangent to a circle from a point outside the circle are ____________!

11. Ex. 3: Find the perimeter of the triangle!
The two segments tangent to a circle from a point outside the circle are ____________!
congruent
Ex. 3: Find the perimeter of the triangle! 8 10 15
P =
P = 66

12. Circle O is inscribed in PQR. PQR has a perimeter of 88cm. Find QY.
x + x = 88 x
64 + 2x = 88 x Y
2x = 24 X
17cm O
x = 12
QY = 12
15cm P R Z
15cm
17cm

13. Homework:
Pg 586-9: # 1 – 22