Question 37
Let $ABΓ$ be a triangle with circumcircle $c(O, R)$, such that $AB \lt AΓ \lt BΓ$ and let $Δ$ be the antipodal point of $B$ with respect to the circle $c$. The perpendicular bisector of $BΔ$ meets $BΓ$ at $K$, $AΓ$ at $M$ and $AB$ at $N$. The line $NΔ$ intersects the circle $c$ at point $T$. Let $Σ$ be the second point of intersection of the circles $c_1(O, Γ, M)$ and $c_2(O, A, Δ)$. Prove that the lines $AΔ$, $ΓT$ and $OΣ$ are concurrent.