Geometry: An Interactive Journey to Mastery



Solutions

10. D௘ͽ &HQWHU PLGSRLQW ͼ௘௘ͽ
    Radius =^1122 AB    ^2212
     (TXDWLRQͼ௘xí௘ͽ^2 ͼ௘yí௘ͽ^2 = 5.
    E௘ͽ
    22
    22
    22

 

6 8 18 77 0

6 9 18 81 5

395.

xx yy

xx y y

xx y y

xy



 

 



It’s the same equation.

F௘ͽ

2211 2 2

11222211 2 2 22

11 2 2 11 2 2 11 2 2

1122 2 2 1 1^22 11 2 22 2 22

112 2

0

0

2222

^22 

2

xa xb ya yb

xabxabyabyab

xyab a b ab a b abab

xyab a b a b aba b ab

xyab a

 

   

§·§ ·§·§· ̈ ̧ ̈ ̧ ̈ ̧ ̈ ̧  

©¹© ¹©¹©¹

§·§ · ̈ ̧ ̈ ̧ 

©¹© ¹

§· ̈ ̧

©¹

2 2 1122 2 2.



§· ̈ ̧b aba b

©¹

This is a circle with center ©¹§· ̈ ̧aba b112 2 22 ,, the midpoint, and radius^

1122 2 2

ab 2 a b,

which is half the distance of AB, as hoped.

Lesson 21

1. Recall that the diagonals of a rhombus bisect one another and
   are perpendicular.
   Suppose that their lengths are 2a and 2b, as shown
   in Figure S.21.1.
   We see four right triangles, each with base a and height b,
   so the area of the rhombus is u^1122 ab ab a b

a

b a

b

Figure S.21.1