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be a circle inscribed inside a rhombus 
. Let 
and 
be variable points on 
and 
respectively, such as 
is always the tangent line to . and the area of triangle 
is the same.
, the points 
and 
are taken such that the point lies between the points 
and , and 
. On segments 
and 
, points and are taken so that 
and 
. Prove that 
.
. On it's sides 
are chosen points 
such that area of 
is half of the area of . Show that at least one of the quadrilaterals 
and 
is parallelogram.
to a unit square, then denote 
. Because affine transform preserves the ratio of areas the area of is still 
. Then 
is twice the sum of areas of 4 small right triangles near the square's angles: 
. Thus either 
or 
. Because affine transform sends parallel lines to parallel lines and intersecting lines to intersecting lines the problem is solved.
