Geometry: An Interactive Journey to Mastery

6. D௘ͽ r 1 = 5 and r 2 = 10.
   E௘ͽ C 1  ͼ௘௘ͽDQGC 2  ͼ௘௘ͽ'LVWDQFH  92212 15.
   F௘ͽ 1RWLFHWKDWWKHGLVWDQFHEHWZHHQWKHFHQWHUVLVWKHVXPRIWKHWZRUDGLL
   7KHWZRFLUFOHVPXVWEHWDQJHQW௘6HHFigure S.20.3௘ͽ


7. D௘ͽ rr 12  DQG   
   E௘ͽ C 1  ͼ௘௘ͽDQGC 2  ͼ௘௘ͽ'LVWDQFH  3223 18 3 2.
   F௘ͽ 1RWLFHWKDWWKHGLVWDQFHEHWZHHQWKHFHQWHUV32, is the
   difference of the two radii:   The two circles
   must be tangent as illustrated in Figure S.20.4.


8. The center of the circle is the midpoint: §· ̈ ̧©¹^152 ,17.
   The radius is half of AB, which equals 22129212  20.
   The equation of the circle is ̈ ̧§·©¹xy ^2172 .


9. )RUͼ௘x௘ͽ^2 ͼ௘yí௘ͽ^2  ZHKDYHC 1  ͼ௘í௘ͽDQGr 1 = 7.
   For
   22
   22
   22

616 370

      

3836

xy x y

xx y y

xy

 

  



we have C 2  ͼ௘í௘ͽDQGr 2 = 6.

The distance between the centers is 512 13^22  rr 12 ,

the sum of the radii.

The two circles must be tangent as shown in Figure S.20.5.

510

Figure S.20.3

2

42

Figure S.20.4

76

Figure S.20.5