000RM.dvi

20.2 Incircle of the shoemaker’s knife 537

20.2 Incircle of the shoemaker’s knife ..........

20.2.1 Archimedes’ construction

Theorem 20.2(Archimedes). The circle tangent to each of the three
semicircles has radius given by

ρ=

ab(a+b)

a^2 +ab+b^2

.

A O 1 O P O 2 B

C

X

Y

Construction

G

H

ABG′ C H′

Z

Y X