MathDB

2 equal rectangles inscribed in square (2020 Kyiv City MO 7.4)

Source:

September 19, 2020

geometryrectanglesquare

Problem Statement

Given a square

ABCD

with side

10

. On sides BC and

AD

of this square are selected respectively points

E

and

F

such that formed a rectangle

ABEF

. Rectangle

KLMN

is located so that its the vertices

K, L, M

and

N

lie one on each segments

CD, DF, FE

and

EC

, respectively. It turned out that the rectangles

ABEF

and

KLMN

are equal with

AB = MN

. Find the length of segment

AL