Question 62
Let $\gamma$, $\gamma_0$, $\gamma_1$, $\gamma_2$ be coplanar circles such that $\gamma_i$ is internally tangent to $\gamma$ at $A_i$, and $\gamma_i$ and $\gamma_{i+1}$ are externally tangent at $B_{i+2}$, $i = 0, 1, 2$ (indices are reduced modulo $3$). The tangent at $B_i$, common to $\gamma_{i-1}$ and $\gamma_{i+1}$, meets $\gamma$ at $C_i$, located in the half-plane opposite $A_i$ with respect to the line $A_{i-1}A_{i+1}$. Show that the three lines $A_iC_i$ are concurrent.
Flavian Georgescu
Flavian Georgescu