000RM.dvi

714 The excircles

26.3 The circumcircle of the excentral triangle ....

The circle through the excenters has center at the reflection of the incen-

ter in the circumcenter, and radius twice the circumradius.

A

B C

Ic

Ia

Ib

O O′

D X′

I

O′Ia=ra+O′X′

=ra+2OD−r

=ra+2(R−DM′)−r (from previous page)

=ra+2R−(ra−r)−r

=2R.

Similarly,O′Ib=O′Ic=2R.