sol = First@
  Solve[{x^2 + y^2 == 184^2, x == -17, y > 0}, {x, y}, Reals]

{{x -> -17, y -> Sqrt[33567]}}

x = 184 - y /. sol

184 - Sqrt[33567]

sol = First@
  Solve[{x^2 + y^2 == 184^2, x == -17, y > 0}, {x, y}, Reals]

{{x -> -17, y -> Sqrt[33567]}}

x = 184 - y /. sol

184 - Sqrt[33567]

Geometric solution

d1 = Disk[{0, 0}, 184];
c1 = d1 /. Disk :> Circle;
r1 = Rectangle[{0, 0}, {-17, 184}];

sol = RegionIntersection[c1, RegionBoundary@r1]

Point[{{0, 184}, {-17, Sqrt[33567]}}]

GraphicsRow[{
  Graphics[{d1, Red, r1, Yellow, AbsolutePointSize@Large, 
    Point@RegionCentroid@d1}]
  , Graphics[{c1, FaceForm[None], EdgeForm[Thick], r1, 
    AbsolutePointSize@Large, Red, sol}
   , PlotRange -> {{-20, 10}, {180, 186}}]
  }]