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Defining the points P_i in triangle ABC so P_6=P_1

Source: Japanese MO Finals 1994

February 11, 2011

analytic geometrygeometry proposedgeometry

Problem Statement

Let

P_0

be a point in the plane of triangle

A_0A_1A_2

. Define

P_i\ (i=1,\ldots ,6)

inductively as the point symmetric to

P_{i-1}

with respect to

A_k

, where

k

is the remainder when

i

is divided by

3

.
a) Prove that

P_6\equiv P_1

. b) Find the locus of points

P_0

for which

P_iP_{i+1}

does not meet the interior of

\triangle A_0A_1A_2

for

0\le i\le 5

.

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