English Információ A lap Pontverseny Cikkek Hírek Fórum

Rendelje meg a KöMaL-t!

VersenyVizsga portál

Kísérletek.hu

Matematika oktatási portál

A. 650. There is given an acute-angled triangle $\displaystyle ABC$ with a point $\displaystyle X$ marked on its altitude starting from $\displaystyle C$. Let $\displaystyle D$ and $\displaystyle E$ be the points on the line $\displaystyle AB$ that satisfy $\displaystyle \sphericalangle DCB=\sphericalangle ACE=90^\circ$. Let $\displaystyle K$ and $\displaystyle L$ be the points on line segments $\displaystyle DX$ and $\displaystyle EX$, respectively, such that $\displaystyle BK=BC$ and $\displaystyle AL=AC$. Let the line $\displaystyle AL$ meet $\displaystyle BK$ and $\displaystyle BC$ at $\displaystyle Q$ and $\displaystyle R$, respectively; finally let the line $\displaystyle BK$ meet $\displaystyle AC$ at $\displaystyle P$. Show that the quadrilateral $\displaystyle CPQR$ has an inscribed circle.

(5 points)

Deadline expired on 10 November 2015.

Statistics on problem A. 650.
 7 students sent a solution. 5 points: Bodnár Levente, Bukva Balázs, Lajkó Kálmán, Szabó 789 Barnabás, Williams Kada. 2 points: 2 students.

• Problems in Mathematics of KöMaL, October 2015

•  Támogatóink: Morgan Stanley