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