MathDB
concurrency wanted , starting with AB + AC = 3 BC

Source: Czech-Polish-Slovak Junior Match 2017, individual p2 CPSJ

February 20, 2020
geometryconcurrencyconcurrent

Problem Statement

Given is the triangle ABCABC, with ∣AB∣+∣AC∣=3⋅∣BC∣| AB | + | AC | = 3 \cdot | BC | . Let's denote D,ED, E also points that BCDABCDA and CBEACBEA are parallelograms. On the sides ACAC and ABAB sides, FF and GG are selected respectively so that ∣AF∣=∣AG∣=∣BC∣| AF | = | AG | = | BC |. Prove that the lines DFDF and EGEG intersect at the line segment BCBC
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