MathDB

Let

ABC

be a triangle with

BA=BC

and

\angle ABC=90^{\circ}

. Let

D

and

E

be the midpoints of

CA

and

BA

respectively. The point

F

is inside of

\triangle ABC

such that

\triangle DEF

is equilateral. Let

X=BF\cap AC

and

Y=AF\cap DB

. Prove that

DX=YD

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