KöMaL problem A, 2019

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Let $k_1,\ldots,k_5$ be five circles in the plane such that $k_1$ and $k_2$ are externally tangent to each other at point $T$ , $k_3$ and $k_4$ are externally tangent to both $k_1$ and $k_2$ , $k_5$ is externally tangent to $k_3$ and $k_4$ at points $U$ and $V$ , respectively, moreover $k_5$ intersects $k_1$ at $P$ and $Q$ , like shown in the figure.

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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.