SAT1000 - P846

Geometry Level pending

As shown above, ON,NMON, NM are rigid rods and DN=ON=1,MN=3DN=ON=1,MN=3, O(0,0)O(0,0) is fixed on the coordinate plane, and DD is restricted along the x-axis. Then as DD moves horizontally, point MM will rotate around point OO. Curve CC is the locus of point MM.

If line ll intersects with l1:x2y=0l_1:x-2y=0 at point PP, l2:x+2y=0l_2:x+2y=0 at point QQ, and ll is tangent to curve CC.

Then find the minimum area of OPQ\triangle OPQ when line ll moves and rotates.

Let SS be the minimum area. Submit 1000S\lfloor 1000S \rfloor.

Have a look at my problem set: SAT 1000 problems


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