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Bundeswettbewerb Mathematik 1994 Problem 1.3

Source: Bundeswettbewerb Mathematik 1994 Round 1

October 9, 2022

Trianglearea of a trianglegeometrymidpoint

Problem Statement

Given a triangle

A_1 A_2 A_3

and a point

P

inside. Let

B_i

be a point on the side opposite to

A_i

for

i=1,2,3

, and let

C_i

and

D_i

be the midpoints of

A_i B_i

and

P B_i

, respectively. Prove that the triangles

C_1 C_2 C_3

and

D_1 D_2 D_3

have equal area.

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