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triangle construction given cuts of <B,<C bisectors with sides + point A

Source: 2012 Sharygin Geometry Olympiad Final Round 8.2

August 3, 2018

geometryangle bisectorconstruction

Problem Statement

In a triangle

ABC

the bisectors

BB'

and

CC'

are drawn. After that, the whole picture except the points

A, B'

, and

C'

is erased. Restore the triangle using a compass and a ruler.
(A.Karlyuchenko)