Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 743. (February 2019)

A. 743. The incircle of tangential quadrilateral $\displaystyle ABCD$ intersects diagonal $\displaystyle BD$ at $\displaystyle P$ and $\displaystyle Q$ ($\displaystyle BP<BQ$). Let $\displaystyle UV$ be the diameter of the incircle perpendicular to $\displaystyle AC$ ($\displaystyle BU<BV$). Show that the lines $\displaystyle AC$, $\displaystyle PV$ and $\displaystyle QU$ pass through one point.

Based on problem 2 of IOM 2018, Moscow

(7 pont)

Deadline expired on March 11, 2019.

### Statistics:

 5 students sent a solution. 7 points: Csaplár Viktor, Nguyen Nguyen, Pooya Esmaeil Akhoondy, Schrettner Jakab, Shuborno Das.

Problems in Mathematics of KöMaL, February 2019