SAT1000 - P594

Geometry Level 3

As shown above, in triangular pyramid ABCDA-BCD, the cross section AEFAEF passes through the center of the inscribed sphere OO (i.e. The sphere which is tangent to all of the faces of the solid) of ABCDA-BCD, and it intersects with BC,DCBC, DC at point E,FE,F respectively.

If the cross section divides the pyramid into two parts whose volumes are equal, S1S_1 is the surface area of solid ABEFDA-BEFD, S2S_2 is the surface area of solid AEFCA-EFC, what is always true for S1S_1 and S2S_2?


Have a look at my problem set: SAT 1000 problems

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