1. SECTION 10.5
Tangents

2. TANGENTS
 How can I use the properties of tangents to solve
problems?

3. TANGENT
 Tangent: A line that intersects the circle in exactly 1
point.

4. THEOREM
 Theorem 10.9: If a line is tangent to a circle, then it
is perpendicular to the radius drawn to the point of
tangency.

5. THEOREM
 Theorem 10.10: If a line is perpendicular to a
radius of a circle, then the line is tangent to the
circle.

6. THEOREM
 Theorem 10.11: If two segments from the same
exterior point are tangent to a circle, then they are
congruent.

7. EXAMPLE

20
y

8. EXAMPLE


9. EXAMPLE


10. EXAMPLE


11. EXAMPLE
 Find x. Assume that segments
that appear tangent to circle
are tangent.

12. EXAMPLE
 Find a. Assume that segments that appear tangent
to circle are tangent.

13. CIRCUMSCRIBED POLYGONS
 Circumscribed Polygon: When a circle is inside a
polygon and every side of the polygon is tangent to
the circle.
 Which one?

14. EXAMPLE


15. HOMEWORK
 Page 556
 #8 – 28 Even, skip 22
 38, 40

16. LESSON PLAN
 Intro
 Define a tangent and its relationship to a circle’s radius
 Standards- 9.5
 Supplies – slides, whiteboard, note sheets
 Timing: One day for notes, one day for a combined
review of 10.5 and 10.6 and a quiz.
 Day 1:
 Essential Questions- slides 2
 Input-slides 3 - 6, 13
 Guided Practice - slides 7 – 12, 14, 15
 Independent Practice – Book Work