1. Tangent/Radius Theorems
11-1 Tangent Lines
Tangent/Radius Theorems
Two Tangents Theorem

2. Vocabulary Tangent to a circle Point of tangency
A line in the same plane of a circle that intersects the circle in exactly one point.
The point where a circle and a tangent intersect.

3. Theorem 11-1
If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. A P B O

4. #1 Finding Angle Measures
is tangent to Find the value of x. D E xo O
38o

5. Theorem 11-2
If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. A P B O

6. #2 Finding a Tangent
A belt fits tightly around two circular pulleys. Find the distance between the centers of the pulleys.
15 cm
3 cm
15 cm
3 cm
4 cm O P x
7 cm
15 cm

7. #3 Finding a Tangent
If NL = 4, LM = 7, and NM = 8, is tangent to a at L? M 8 7 4 L N

8. Vocabulary Inscribed in Circumscribed about
All vertices of a figure lie on the circle.
When a circle is inscribed in a figure.

9. Theorem 11-3
The two segments tangent to a circle from a point outside the circle are congruent. A B O C

10. #4 Circles Inscribed in Polygons
Circle O is inscribed in Triangle PQR. Triangle PQR has a perimeter of 88 cm. Find QY. Q x X x
15 cm P Y O
15 cm Z
17 cm
17 cm R