Warm Up

1
Warm Up

• p. 17817

2
Tangents/Circumscribed Polygons

• Section 3-7/3-8

• Today we will
• Learn the definition of a tangent along with
  theorems that can be
• Used to find missing measures
• Learn formulas for circumscribed polygons that
  allow us to find
• Its perimeter

3
Tangents

• Tangent Line in a plane of a circle that
  intersects the circle at exactly one point

4
Tangent Theorems
Theorem 3.10 If a line is tangent to a circle
then the line is perpendicular the radius from
the center of the circle to the point of tangency.

Theorem 3.11 If a line in a plane of a circle is
perpendicular to the radius at its outer endpoint
then it is tangent to the circle.
5
Tangent Theorems Continued
Theorem 3.12 If 2 tangent lines are drawn from
the same point to the same circle then they are
equal in measure
6
Example
Given YR and YC are tangents to circle O OC
10 CY 19.6 Angle CYR 54o Find angles CYO
and RYO Segments OP, RY, PY
C
Y
P
O
R
Triangle CYO congruent to RYO (SSS) Angle CYO
RYO ½ (54o) 27o OP 10 (radius) RY 19.6
(Theorm 3.12)
PY OY OP gt 22-10 12
7
Circumscribed Polygons

• Polygons with a circle inscribed
• The sides of the circumscribed polygon are
  tangents to the inscribed circle

8
Area of circumscribed polygons
Semiperimeter ½ perimeter of a polygon Area of
circumscribed polygon rs, where r is the radius
of the inscribed circle and s is the
semiperimeter of the circumscribed polygon
6
4
Perimeter 4 6 10 7 8 35 Semiperimeter
½ 35 17. 5 Area rs 5 17.5 87.5
10
5
7
8

• .

9
Example
GivenRadius 10 GD 4 DI 3 AB 7 BN
5 Find GR, IE, AR and EN Find Area GINA
G
D
I
R
O
E
A
B
N
GR GD 4 (tangent theorem) IE ID 3
(tangent theorem) AR AB 7 (tangent
theorem) EN BN 5 (tangent theorem) Area
rs Perimeter 4 4 3 3 7 7 5 5
8 6 14 10 38 Area ½ 38 10 19
10 190
10
Homework
P. 189 1,2,4, 5 (one method only) Worksheet