Solve (x_{1}-h)^2+(y_{1}-k)^2<r^2

$$( x _ { 1 } - h ) ^ { 2 } + ( y _ { 1 } - k ) ^ { 2 } < r ^ { 2 }$$

Solve for y_1

$$y_{1}\in \left(-\sqrt{-\left(x_{1}-h\right)^{2}+r^{2}}+k,\sqrt{-\left(x_{1}-h\right)^{2}+r^{2}}+k\right)$$

$$\left(x_{1}>h+r\text{ and }x_{1}<h-r\right)\text{ or }\left(x_{1}>h-r\text{ and }x_{1}<h+r\right)\text{ or }\left(x_{1}>h-|r|\text{ and }x_{1}<|r|+h\text{ and }x_{1}\leq h-r\text{ and }x_{1}\geq h+r\right)\text{ or }\left(x_{1}>h-|r|\text{ and }x_{1}<|r|+h\text{ and }x_{1}\leq h+r\text{ and }x_{1}\geq h-r\right)$$

Solve for x_1

$$x_{1}\in \left(-\sqrt{-\left(y_{1}-k\right)^{2}+r^{2}}+h,\sqrt{-\left(y_{1}-k\right)^{2}+r^{2}}+h\right)$$

$$\left(y_{1}>k-r\text{ and }y_{1}<k+r\right)\text{ or }\left(y_{1}>k+r\text{ and }y_{1}<k-r\right)\text{ or }\left(y_{1}>k-|r|\text{ and }y_{1}<|r|+k\text{ and }y_{1}\geq k+r\text{ and }y_{1}\leq k-r\right)\text{ or }\left(y_{1}>k-|r|\text{ and }y_{1}<|r|+k\text{ and }y_{1}\geq k-r\text{ and }y_{1}\leq k+r\right)$$