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2021 Geo Div 2 P5

Source:

March 2, 2021
geometry

Problem Statement

Emily is at (0,0)(0,0), chilling, when she sees a spider located at (1,0)(1,0)! Emily runs a continuous path to her home, located at (2+2,0)(\sqrt{2}+2,0), such that she is always moving away from the spider and toward her home. That is, her distance from the spider always increases whereas her distance to her home always decreases. What is the area of the set of all points that Emily could have visited on her run home?
Proposed by Thomas Lam
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