KöMaL 2010 B4236

Let $a$ , $b$ and $c$ be the sides of triangle $ABC$ , let $f_a$, $f_b$ and $f_c$ denote the lengths of the interior angle bisectors, and let $t_a$, $t_b$ and $t_c$ be the segments of the interior angle bisectors that lie inside the circumscribed circle. Show that $a^2b^2c^2= f_af_bf_ct_at_bt_c$.