20.3 More Archimedean circles 541
Exercise
1.The circles(C 1 )and(C 1 ′)are each tangent to the outer semicircle
of the shoemaker’s knife, and toOQ 1 atQ 1 ; similarly for the circles
(C 2 )and(C 2 ′). Show that they have equal radiit=aab+b.
C 1
C 2
C 1 ′
C′ 2
A O 1 O P O 2 B
Q 1
Q 2
2.We call the semicircle with diameterO 1 O 2 themidwaysemicircle
of the shoemaker’s knife.
Show that the circle tangent to the linePQand with center at the
intersection of(O 1 )and the midway semicircle has radiust=aab+b.
C
C′
A O 1 O P O 2 B
Q
3.Show that the radius of the circle tangent to the midway semicircle,
the outer semicircle, and with center on the linePQhas radius
t=aab+b.
C
A O 1 O P O 2 B
Q