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concurrent wanted, 2 circles each ecternal to other one related

Source: 1961 Hungary - Kürschák Competition p3

October 11, 2022
concurrentgeometry

Problem Statement

Two circles centers OO and OO' are disjoint. PPPP' is an outer tangent (with PP on the circle center O, and P' on the circle center OO'). Similarly, QQQQ' is an inner tangent (with QQ on the circle center OO, and QQ' on the circle center OO'). Show that the lines PQPQ and PQP'Q' meet on the line OOOO'. https://cdn.artofproblemsolving.com/attachments/b/d/bad305631571323a61b097f149a1bb6855cdc5.png