MathDB

Quadrilateral

ABCD

is inscribed in a circle such that the midpoints of its sides also lie on a (different) circle. Let

M

and

N

be the midpoints of

\overline{AB}

and

\overline{CD}

respectively, and let

P

be the foot of the perpendicular from the intersection of

\overline{AC}

and

\overline{BD}

onto

\overline{BC}

. If the side lengths of

ABCD

are

1

3

\sqrt 2

, and

2\sqrt 2

in some order, compute the greatest possible area of the circumcircle of triangle

MNP

.
Proposed by Connor Gordon

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