MathDB

{ABCD}

is a quadrilateral,

{P}

and

{Q}

are midpoints of the diagonals

{BD}

and

{AC}

, respectively. The lines parallel to the diagonals originating from

{P}

and

{Q}

intersect in the point

{O}

. If we join the four midpoints of the sides,

{X}

{Y}

{Z}

, and

{T}

, to

{O}

, we form four quadrilaterals:

{OXBY}

{OYCZ}

{OZDT}

, and

{OTAX}

. Prove that the four newly formed quadrilaterals have the same areas.

Problem Statement