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Bundeswettbewerb Mathematik 1980 Problem 1.2

Source: Bundeswettbewerb Mathematik 1980 Round 1

September 23, 2022

geometrybisectorsdistanceTriangle

Problem Statement

In a triangle

ABC

, the bisectors of angles

A

and

B

meet the opposite sides of the triangle at points

D

and

E

, respectively. A point

P

is arbitrarily chosen on the line

DE

. Prove that the distance of

P

from line

AB

equals the sum or the difference of the distances of

P

from lines

AC

and

BC