MathDB

Suppose two convex quadrangles in the plane

P

and

P'

, share a point

O

such that, for every line

l

trough

O

, the segment along which

l

and

P

meet is longer then the segment along which

l

and

P'

meet. Is it possible that the ratio of the area of

P'

to the area of

P

is greater then

1.9

Problem Statement