Mathematical and Physical Journal
for High Schools
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# Problem B. 4800. (May 2016)

B. 4800. $\displaystyle T$ is a point on line $\displaystyle BC$, different from the midpoint of line segment $\displaystyle BC$. Circle $\displaystyle k$ is centred at $\displaystyle T$, and $\displaystyle A$ is its intersection with the perpendicular drawn to $\displaystyle BC$ at $\displaystyle T$. The intersections of $\displaystyle k$ with the lines $\displaystyle AB$ and $\displaystyle AC$ are $\displaystyle K$ and $\displaystyle L$, respectively. Let $\displaystyle k$ intersect the circumscribed circle of $\displaystyle ABC$ again at $\displaystyle M$. Prove that the lines $\displaystyle KL$, $\displaystyle AM$ and $\displaystyle BC$ are concurrent.

Proposed by K. Williams, Szeged

(5 pont)

Deadline expired on June 10, 2016.

### Statistics:

 44 students sent a solution. 5 points: Andó Angelika, Horváth András János, Janzer Orsolya Lili, Klász Viktória, Matolcsi Dávid, Nagy Dávid Paszkál, Németh 123 Balázs, Polgár Márton, Schrettner Bálint, Szemerédi Levente. 4 points: Baran Zsuzsanna, Bukva Balázs, Cseh Kristóf, Döbröntei Dávid Bence, Fuisz Gábor, Gáspár Attila, Glattfelder Hanna, Hansel Soma, Harsányi Benedek, Imolay András, Kerekes Anna, Keresztfalvi Bálint, Kocsis Júlia, Kovács 162 Viktória, Lakatos Ádám, Tóth Viktor, Váli Benedek, Vári-Kakas Andor. 3 points: 13 students. 2 points: 1 student. 1 point: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, May 2016