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 Areas equalizer (Posted on 2018-04-28)
Inside a convex quadrilateral ABCD there are points P (and P', P'' etc))such that drawing WP,XP,YP,ZP one gets four quadrilaterals of equal areas (W, X, Y, Z being the midpoints of the sides).

Define P's location.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Convex? I snap my fingers - thus! Comment 1 of 1

Say W is on AB, X is on BC, Y is on CD, and Z is on AD.

If W, X, Y, Z are the midpoints of the sides then WXYZ is the Varignon parallelogram. https://en.wikipedia.org/wiki/Varignon%27s_theorem

Construct lines through A,B,C, and D parallel to WZ, WX, XY, and YZ. These lines intersect to form a new parallelogram, STUV.

The diagonals of STUV intersect at P.

Even if the quadrilateral is concave, or crossed.

 Posted by broll on 2018-04-28 23:55:50

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