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Find the side lengths of triangle

Source: China TST 2003

June 29, 2006

geometrycircumcirclegeometry proposed

Problem Statement

In triangle

ABC

,

AB > BC > CA

,

AB=6

,

\angle{B}-\angle{C}=90^o

. The incircle touches

BC

at

E

and

EF

is a diameter of the incircle. Radical

AF

intersect

BC

at

D

.

DE

equals to the circumradius of

\triangle{ABC}

. Find

BC

and

AC

.

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