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triangle by equal segments on triangles' extensions (2023 Auckland MO p2)

Source:

March 26, 2024

geometryareas

Problem Statement

Triangle

ABC

of area

1

is given. Point

A'

lies on the extension of side

BC

beyond point

C

with

BC = CA'

. Point

B'

lies on extension of side

CA

beyond

A

and

CA = AB'

.

C'

lies on extension of

AB

beyond

B

with

AB = BC'

. Find the area of triangle

A'B'C'

.

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