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Longest line to cut a square into a 20:23 ratio

Source: Indonesia Regional 2023 Essay Number 1

July 16, 2023

geometryratioIndonesiaareaRMO

Problem Statement

Let

ABCD

be a square with side length

43

and points

X

and

Y

lies on sides

AD

and

BC

respectively such that the ratio of the area of

ABYX

to the area of

CDXY

is

20 : 23

. Find the maximum possible length of

XY

.

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