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Prove that the segments are proportional

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September 14, 2010
geometry

Problem Statement

Let A1A2,B1B2,C1C2A_1A_2,B_1B_2, C_1C_2 be three equal segments on the three sides of an equilateral triangle. Prove that in the triangle formed by the lines B2C1,C2A1,A2B1B_2C_1, C_2A_1,A_2B_1, the segments B2C1,C2A1,A2B1B_2C_1, C_2A_1,A_2B_1 are proportional to the sides in which they are contained.
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