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, 2019

Geometry Difficulty 8.0 Shortlist Prove it Hungary

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

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Source: KöMaL, licensed Rights held by KöMaL and the MATFUND Foundation. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.