Mathematical and Physical Journal
for High Schools
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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.


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