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GRE
GRE Quantitative Reasoning Section

Point Location Relative to Circle

Hard Geometry Circles

In the Cartesian plane, consider a circle with center at the point (2, -3) and a radius of 5. The equation of this circle can be expressed in standard form as $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius.

A point is considered to lie inside the circle if it satisfies the inequality $$(x - h)^2 + (y - k)^2 < r^2$$ and outside the circle if it satisfies $$(x - h)^2 + (y - k)^2 > r^2$$.

Determine whether the point (6, -1) lies inside, on the boundary, or outside the circle.

Hint

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