MathDB

Paper-folding trisectors

Source: Brazil Math Olympiad - 2000

March 3, 2006

geometrygeometric transformationreflectiongeometry proposed

Problem Statement

A rectangular piece of paper has top edge

A

. A line

L

from

A

to the bottom edge makes an angle

x

with the line

AD

. We want to trisect

x

. We take

B

and

C

on the vertical ege through

A

such that

AB = BC

. We then fold the paper so that

C

goes to a point

C'

on the line

L

and

A

goes to a point

A'

on the horizontal line through

B

. The fold takes

B

to

B'

. Show that

AA'

and

AB'

are the required trisectors.

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