MathDB

165

Part of 1949 Moscow Mathematical Olympiad

Problems(1)

MMO 165 Moscow MO 1949 locus, 2 triangles, parallelogram related

Source:

7/20/2019
Consider two triangles, ABCABC and DEFDEF, and any point OO. We take any point XX in △ABC\vartriangle ABC and any point YY in △DEF\vartriangle DEF and draw a parallelogram OXYZOXY Z. Prove that the locus of all possible points ZZ form a polygon. How many sides can it have? Prove that its perimeter is equal to the sum of perimeters of the original triangles.
geometryparallelogramLocuspolygonperimeter