Question 73
In the scalene triangle $ABC$, the in-circle touches side *BC* at the point *D*. The angle bisectors of $\angle ABC$ and $\angle ACB$ meet the circumcircle of the triangle at the points $T_B$ and $T_C$, respectively. Let $AX_B$ and $AX_C$ be diameters in the circumcircles of triangles $ACD$ and $ABD$, respectively. Prove that the triangles $BT_CX_C$ and $CT_BX_B$ are similar.