Circles! oh no!!!

Geometry Level 4

Ifachordofthecirclex2+y24x2yc=0istrisectedatthepoints(13,13)and(83,83),thentheradiusofthecirclewillbeIf\quad a\quad chord\quad of\quad the\quad circle\quad { x }^{ 2 }+{ y }^{ 2 }-4x-2y-c=0\\ is\quad trisected\quad at\quad the\quad points\quad \left( \frac { 1 }{ 3 } ,\frac { 1 }{ 3 } \right) \quad and\quad \\ \left( \frac { 8 }{ 3 } ,\frac { 8 }{ 3 } \right) ,\quad then\quad the\quad radius\quad of\quad the\quad circle\quad will\quad be

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