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locus of P if A'BC, AB'C and ABC' are congruent to ABC

Source: Austrian Federal Competition For Advanced Students 2009, Part 2, p3

August 31, 2019

geometryLocuscongruent triangles

Problem Statement

Let

P

be the point in the interior of

\vartriangle ABC

. Let

D

be the intersection of the lines

AP

and

BC

and let

A'

be the point such that

\overrightarrow{AD} = \overrightarrow{DA'}

. The points

B'

and

C'

are defined in the similar way. Determine all points

P

for which the triangles

A'BC, AB'C

, and

ABC'

are congruent to

\vartriangle ABC