Question 82
Let $I$ be the incenter of a triangle $ABC$. Let $A_1$, $B_1$, $C_1$ be the tangency points of the incircle of the triangle $ABC$ with the sides $BC$, $CA$, $AB$, respectively. Let the circumcircle of the triangle $BC_1B_1$ intersect the line $BC$ at points $B$ and $K$, and the circumcircle of the triangle $CB_1C_1$ intersect the line $BC$ at points $C$ and $L$.
Prove that the lines $LC_1$, $KB_1$, $IA_1$ are concurrent.
(A. Voidelevich)
Prove that the lines $LC_1$, $KB_1$, $IA_1$ are concurrent.
(A. Voidelevich)