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3 perpendicular bisectors of PS tangent to a circle

Source: Netherlands - Dutch NMO 1963 p1

January 31, 2023
geometryperpendicular bisectortangent

Problem Statement

In a plane are given a straight line ℓ\ell and a point PP not located on ℓ\ell. Is there a circle in this plane such that there exist more than three different points SS on ℓ\ell with the property that the perpendicular bisector of PSPS is tangent to the circle ? Explain the answer.
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