Question 62
The angle bisectors of an acute triangle $ABC$ meet at point $I$. The line $AI$ meets the circumcircle of the triangle $ABC$ at point $D$ ($D \neq A$) and the side $BC$ at point $E$. The line $BI$ meets the circumcircle of the triangle $CDI$ at point $K$ whereas the line $CI$ meets the circumcircle of the triangle $BDI$ at point $L$ ($K \neq I, L \neq I$).
a. Prove that the line $DI$ is tangent to the circumcircle of the triangle $IKL$.
b. Prove that points $A, K, L, E$ are concyclic.
a. Prove that the line $DI$ is tangent to the circumcircle of the triangle $IKL$.
b. Prove that points $A, K, L, E$ are concyclic.