1. To recognize tangents and use the properties of tangents

2. Definition Tangent – A line that intersects a circle in exactly 1 pt.
Pt of tangency – Pt where a tangent line intersects a circle
Secant – A line that intersects a circle in 2 pts
A circle separates a plane into 3 parts
interior
exterior
circle
Secant
Pt of tangency
Tangent line

3. Theorem
If a line is tangent to a circle , then it is perpendicular to the radius drawn to the pt of tangency
Converse – If a line is perpendicular to a radius of a circle at the end pt on the circle, then the line is a tangent of the circle

4. Example ALGEBRA is tangent to at point R. Find y.
Answer: Thus, y is twice

5. Example
Is AB tangent to circle C?
ST is tangent to oQ.
Find r A B 5 4 2 C 24 18 r Q S T No
= 52
242 + r2 = (18 + r)2
576 + r2 = r + r2
576 = r
252 = 36r
7 = r

6. Definition:
Common tangent – a line or line segment that is tangent to 2 circles in the same plane
There are 2 types of common tangents
Common external tangents
Common internal tangents
Tangents do not intersect the segment connecting the centers of the circle
Tangents intersect the segment connecting the centers

7. Theorem
If 2 segments from the same exterior pt are tangent to a circle, then they are congruent

8. Example ED congruent FD…so y = 10 EG is congruent to FH…so
ALGEBRA Find x. Assume that segments that appear tangent to circles are tangent.
ED congruent FD…so y = 10
EG is congruent to FH…so
y - 5 = x + 4
10 – 5 = x + 4
5 = x + 4
1 = x

9. Example: Find C 2c2 +9c + 6 9c + 14 2c2 + 9c + 6 = 9c + 14
c = 2 and -2
Can’t be -2 because that will make the
segment – in length

10. Circumscribed Polygons
A polygon is circumscribed about a circle, if each side of the polygon is tangent to the circle

11. Example Answer: 158 units 16 16+29 18 16 + 29
Triangle HJK is circumscribed about Find the perimeter of HJK if 16
16+29 18
Answer: 158 units

12. Homework
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Pg – 10, 15 – 26