Points of Authority

Geometry Level pending

Consider the rectangle \( ABCD \) and points \(M, N, O, P \) on the segments \( \overline{AB}\), \( \overline{BC}\), \(\overline{CD} \) and \(\overline{AD} \), respectively.

\(MO \) and \( NP\) are perpendicular to each, intersecting at the point \( X \).

If \(\left [ AMXP \right ] = 6, \left [ PXOD \right ]= 8 \) and \( \left [ MBNX \right ] = 18 \) , evaluate \(\left [ MNOP \right ] + \left [ ABCD \right ] \).

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