Transcript 11-1 Tangent Lines - Mrs.Lemons Geometry

11-1
Tangent Lines
Objective: To use the relationship
between two tangents from one
point.
Vocabulary
• Inscribed in
• Circumscribed about
• All vertices of a figure
lie on the circle.
• When a circle is
inscribed in a figure.
#1 Finding a Tangent
• A belt fits tightly around two circular
pulleys. Find the distance between the
centers of the pulleys.
4  15  x
2
16  225  x
2
2
241  x
x  15.5 cm
2
15 cm
3 cm
3 cm
15 cm
O
x
4 cm
P
7 cm
15 cm
#2 Finding a Tangent
A belt fits tightly around
two circular pulleys, as
shown. Find the distance
between the centers of the
pulleys.
35 cm
14 cm
8 cm
O
35  6  OP
2
1225 36  OP
2
1261 OP
35 .5  OP
2
2
2
35 cm
6 cm
P
Theorem 11-3
• The two segments tangent to a circle from
a point outside the circle are congruent.
A
B
AB  CB
O
C
#3 Circles Inscribed in Polygons
• Circle O is inscribed in Triangle PQR.
Triangle PQR has a perimeter of 88 cm.
Find QY.
88  15  15  x  x  17  17
88  30  2 x  34
88  64  2 x
24  2 x
x  12 cm
Q
x
X
x
15 cm
P
Y
O
15 cm
Z
17 cm
17 cm
R
#4 Circles Inscribed in Polygons
• Circle O is inscribed in Triangle ABC. Find
the Perimeter of Triangle ABC.
AD  AF  10cm
BD  BE  15cm
CF  CE  8cm
p  10  15  15  8  8  10
p  66
B
15cm
D
15cm
10 cm
A
E
O
10 cm
F
8 cm
8 cm
C
Assignment
•Page 586
•#4-9; 13-19