MathDB

The diagonals

AC{}

and

BD

of the trapezoid

ABCD

intersect at

E{}.

The bisector of the angle

BEC

intersects the bases

BC

and

AD

X{}

and

Z{}

. The perpendicular bisector of the segment

XZ

intersects the sides

AB

and

CD

Y{}

and

T{}

. Prove that

XYZT{}

is a rhombus.
Proposed by M. Didin, I. Kukharchuk and P. Puchkov

Problem Statement