Question 66
Let $ABCD$ be a cyclic quadrilateral, $P = AB \cap CD$, $Q = AD \cap BC$.
Prove that the distance between the orthocenters of the triangles $APD$ and $AQB$ is equal to that of the triangles $CQD$ and $BPC$.
Editorial metadata note: Metadata discrepancy: the dataset year is 2014, while booklet_year is 2015. The title follows dataset classification, not a verified Belarus 2014 event date.
Prove that the distance between the orthocenters of the triangles $APD$ and $AQB$ is equal to that of the triangles $CQD$ and $BPC$.
Editorial metadata note: Metadata discrepancy: the dataset year is 2014, while booklet_year is 2015. The title follows dataset classification, not a verified Belarus 2014 event date.