Let SABC be a regular pyramid, O the center of basis ABC, and M the midpoint of [BC]. If N∈[SA] such that SA=25⋅NS and SO∩MN={P}, AM=2⋅SO, prove that the planes (ABP) and (SBC) are perpendicular.
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Tags: geometry, 3D geometry, pyramid
Let SABC be a regular pyramid, O the center of basis ABC, and M the midpoint of [BC]. If N∈[SA] such that SA=25⋅NS and SO∩MN={P}, AM=2⋅SO, prove that the planes (ABP) and (SBC) are perpendicular.