Minimal Distance

Geometry Level 4

Consider the circle Γ\Gamma whose equation is x2+y228x+40y+20=0x^2 + y^2- 28x + 40y + 20 = 0. Let SS be the set of all points PP outside Γ\Gamma such that if there is a line through PP which intersects Γ\Gamma at two points AA and BB, then PAPB=100PA\cdot PB = 100. Find the minimum possible distance between a point on Γ\Gamma and a point on SS.

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