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3 line segments divide a triangle into 5 triangles, inequality area problem

Source: 2016 VWO Flanders MO p3

August 7, 2020
geometryareasGeometric Inequalities

Problem Statement

Three line segments divide a triangle into five triangles. The area of these triangles is called u,v,x,u, v, x, yand zz, as in the figure. (a) Prove that uv=yzuv = yz. (b) Prove that the area of the great triangle is at most xzy \frac{xz}{y} https://cdn.artofproblemsolving.com/attachments/9/4/2041d62d014cf742876e01dd8c604c4d38a167.png
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