SAT1000 - P838

Geometry Level pending

As shown above, the ellipse has equation: x2+y22=1x^2+\dfrac{y^2}{2}=1, F(0,1)F(0,1), line l:y=2x+1l: y=-\sqrt{2} x + 1 intersects with the ellipse at point A,BA,B, and PP is a point on the ellipse so that OA+OB+OP=0\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OP}=\textbf 0.

Point P,QP,Q are symmetry about point OO, and it turns out A,P,B,QA,P,B,Q are on the same circle.

The radius of the circle is rr. Submit 1000r\lfloor 1000r \rfloor.


Have a look at my problem set: SAT 1000 problems

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