MathDB

9.1

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

unit square and a circle (IV Soros Olympiad 1997-98 Correspondence 9.1)

Source:

6/1/2024
Through vertices AA and BB of the unit square ABCDABCD , passes a circle intersecting lines ADAD and ACAC at points KK and MM, other than AA. Find the length of the projection KMKM onto ACAC.
geometry
2(x-6)=x^2/ (1+\sqrt{x+1})^2 (IV Soros Olympiad 1997-98 R3 9.1)

Source:

6/1/2024
Solve the equation 2(x−6)=x2(1+x+1)22(x-6)=\dfrac{x^2}{(1+\sqrt{x+1})^2}
algebraRadicals
football tournament (IV Soros Olympiad 1997-98 R2 9.1)

Source:

6/1/2024
The football tournament was played in one round. 33 points were given for a win, 11 point for a draw, and 00 points for a loss. Could it be that the first place team under the old scoring system (win - 22 points, draw - 11 point, loss - 00) would be last?
algebranumber theory