MathDB

5

Part of 2021 Czech-Polish-Slovak Junior Match

Problems(2)

<PDG =? in regular hexagon ABCDEFG , AB and CE meet at P

Source: Czech-Polish-Slovak Match Junior 2021, individual p5 CPSJ

9/12/2021
A regular heptagon ABCDEFGABCDEFG is given. The lines ABAB and CECE intersect at P P. Find the measure of the angle ∠PDG\angle PDG.
angleshexagongeometry
x/y + y/z + z/x = x/z + z/y + y/x , x^2 + y^2 + z^2 = xy + yz + zx + 4

Source: 2021 Czech-Polish-Slovak Match Junior, team p5 CPSJ

9/12/2021
Find all three real numbers (x,y,z)(x, y, z) satisfying the system of equations xy+yz+zx=xz+zy+yx\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=\frac{x}{z}+\frac{z}{y}+\frac{y}{x} x2+y2+z2=xy+yz+zx+4x^2 + y^2 + z^2 = xy + yz + zx + 4
algebrasystem of equations