Geo_Book_Answers

Answers to Exercises
Answers to Exercises
CHAPTER 6 • CHAPTER CHAPTER 6 • CHAPTER
LESSON 6.1
1. 50° 2. 55°
3. 30° 4. 105°
5. 76 in.
6. possible answer:
7. Possible answer: The perpendicular to the
tangent passes through the center of the circle. Use
the T-square to find two diameters of the Frisbee.
The intersection of these two lines is the center.
8. Construct OT . Construct a line through point T
perpendicular to OT .
9. Construct OX ,OY , and OZ . Construct tangents
through points X, Y, and Z.
X
O
Z
r
10. Construct tangent circles M and N. Construct
equilateral MNP.Construct circle P with radius s.
s s
M N
P
O
74 ANSWERS TO EXERCISES
T
t Y
6
Target
11. Construct a line and label a point T on it. On
the line, mark off two points, L and M, each on
the same side of T at distances r and t from T,
respectively. Construct circle L with radius r.
Construct circle M with radius t.
r
L M T
t
12. Start with the construction from Exercise 11.
On line LM , mark off length TK so that TK s
and K is on the opposite side of T from L and M.
Construct circle K with radius s.
r
L M T K
t s
13. Sample answer: If the three points do not lie
on the same semicircle, the tangents form a circumscribed
triangle. If two of the three points are
on opposite sides of a diameter, the tangent lines to
those two points are parallel. If the points lie on the
same semicircle, they form a triangle outside the
circle, with one side touching (called an exscribed
triangle).
14. sample answer: internally tangent: wheels on a
roller-coaster car in a loop, one bubble inside
another; externally tangent: touching coins, a
snowman, a computer mouse ball and its roller
balls
15. Constructions will vary.
16. 360° 30° 90° 90° 150° and
150°
360°
41.6%
17. Angles A and B must be right angles, but this
would make the sum of the angle measures in the
quadrilateral shown greater than 360°.
18a. rhombus 18b. rectangle
18c. kite 18d. parallelogram
19. 78° 20. 9.7 km
21. x 55° 55° 180° and 40° y
y 180°, so x y 70°
22. 11
21