Circles Γ₁ and Γ₂ ( with centers O₁ and O₂ respectively ) intersect
at points A and B such that neither center lies on or inside the other circle.
Lines m_A and m_B are tangent to circle Γ₁ at points A and B respectively.

Distinct points C and D lie on Γ₂ ∩ H(A,m_B) ∩ H(B,m_A), where H(X,m_Y)
denotes the open half-plane determined by the line m_Y and does not contain point X.

Rays CA, CB, DA, and DB intersect Γ₁ at points C_A, C_B, D_A, and D_B
respectively.

   I = C_AD_A ∩ C_BD_B
                and
   J = C_AC_B ∩ D_AD_B

Prove that points I, J, and O₁ are collinear.