Mathematical and Physical Journal
for High Schools
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Problem C. 1334. (January 2016)

C. 1334. Given that the cyclic quadrilateral \(\displaystyle ABCD\) is either a trapezium (where \(\displaystyle AB\parallel CD\)) or its side \(\displaystyle AB\) is a diameter of the circumscribed circle, then the equations

\(\displaystyle BD\cdot x+AD\cdot \sqrt{1-x^2} = AC;\)

\(\displaystyle AC\cdot x+BC\cdot \sqrt{1-x^2} = BD\)

are held for some \(\displaystyle x\) of \(\displaystyle 0<x<1\).

(5 pont)

Deadline expired on February 10, 2016.


Statistics:

25 students sent a solution.
5 points:Csorba Benjámin, Gera Dóra, Horváth András János, Kocsis Júlia, Komoróczy Ádám, Kormányos Hanna Rebeka, Kósa Szilárd, Matusek Márton, Mészáros 01 Viktória, Nagy 911 Viktória, Szajkó Gréta, Tatai Mihály, Tóth Adrián.
4 points:Csapó Márton, Kasó Ferenc, Sudár Ákos, Szücs Patrícia, Tar Viktor.
3 points:1 student.
2 points:3 students.
0 point:3 students.

Problems in Mathematics of KöMaL, January 2016