Suppose we have an acute triangle $\displaystyle PQR$.

Let the bisector of each individual angle meet the circumcircle (for the second time). Let the points of intersection be $\displaystyle P_1$, $\displaystyle Q_1$, $\displaystyle R_1$.

$\displaystyle PQ$ and $\displaystyle Q_1R_1$ intersect at A.

$\displaystyle QR$ and $\displaystyle P_1Q_1$ intersect at B.

Prove that the incentre, A, and B, are collinear.