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Why is this a triangle geometry problem?

Source: Problem 3 of the German pre-TST 2004, written in December 03

February 28, 2004
geometryanalytic geometrycircumcircleincentertrigonometryratioconics

Problem Statement

Given six real numbers aa, bb, cc, xx, yy, zz such that 0<bāˆ’c<a<b+c0 < b-c < a < b+c and ax+by+cz=0ax + by + cz = 0.
What is the sign of the sum ayz+bzx+cxyayz + bzx + cxy ?
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