SAT1000 - P845

Geometry Level 4

As shown above, the parabola E:y2=xE: y^2=x and circle M:(x4)2+y2=r2M: (x-4)^2+y^2=r^2 for r>0r>0 intersect at points AA, BB, CC, and DD; and their relative positions are shown in the figure. Lines ACAC and BDBD intersect at point PP.

Find the coordinates (x0,0)(x_0,0) of PP as the area of quadrilateral ABCDABCD reaches the maximum when rr varies. Submit 1000x0\lfloor 1000x_0 \rfloor.


Have a look at my problem set: SAT 1000 problems

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