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|Where's the Center (Posted on 2018-05-20)
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 mA and mB are tangent to circle Γ1 at points A and B respectively.
Distinct points C and D lie on Γ2 ∩ H(A,mB) ∩ H(B,mA), where H(X,mY)
denotes the open half-plane determined by the line mY and does not contain point X.
Rays CA, CB, DA, and DB intersect Γ1 at points CA, CB, DA, and DB
I = CADA ∩ CBDB
J = CACB ∩ DADB
Prove that points I, J, and O1 are collinear.
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