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Imagine trying synthetic

Source: 2022 USAJMO 4

March 24, 2022

geometrycoordinate geometryUSAJMOUSAgeometry solvedAMCUSA(J)MO

Problem Statement

Let

ABCD

be a rhombus, and let

K

and

L

be points such that

K

lies inside the rhombus,

L

lies outside the rhombus, and

KA = KB = LC = LD

. Prove that there exist points

X

and

Y

on lines

AC

and

BD

such that

KXLY

is also a rhombus.
Proposed by Ankan Bhattacharya