Let I=X(1) incenter of ABC. Circle BIC ıntersects the AC and AB at Ab, Ac. Define Ba,Bc, Ca,Cb cyclically.
Inversion of the line BC in the circle (IBcCb) is a cirlcle GammaA. Define GammB, GammaC cyclically.* GammaA, GammB, GammaC are concurrent circles. Concurrency point is X(5497) = 5th HATZIPOLAKIS-MONTESDEOCA POINT.
Instead of I if we use S=X(15)-1st isodynamic point GammaA, GammaB and GammaC concur at X(5612).
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