MathDB

2

Part of 2017 Czech-Polish-Slovak Junior Match

Problems(2)

concurrency wanted , starting with AB + AC = 3 BC

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

2/20/2020
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
geometryconcurrencyconcurrent
convex hexagon with sides >1 and 9 diagonals >2

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

3/6/2020
Decide if exists a convex hexagon with all sides longer than 11 and all nine of its diagonals are less than 22 in length.
hexagondiagonalsgeometry