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conctruction of point F on arc AB , PE/EQ = m/n

Source: XI All-Ukrainian Tournament of Young Mathematicians, Qualifying p4

May 27, 2021
geometryconstructionarcratioUkrainian TYM

Problem Statement

Chords ABAB and CDCD, which do not intersect, are drawn in a circle. On the chord ABAB or on its extension is taken the point EE. Using a compass and construct the point FF on the arc ABAB , such that PEEQ=mn\frac{PE}{EQ} = \frac{m}{n}, where m,nm,n are given natural numbers, PP is the point of intersection of the chord ABAB with the chord FCFC, QQ is the point of intersection of the chord ABAB with the chord FDFD. Consider cases where E∈PQE\in PQ and E∉PQE \notin PQ.
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