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angles between segments defined by points on tangents of regular hexagons

Source: Sharygin Geometry Olympiad 2016 First Round P19 grades 9-11

July 25, 2018

geometrycircumcircleregular polygonhexagon

Problem Statement

Let

ABCDEF

be a regular hexagon. Points

P

and

Q

on tangents to its circumcircle at

A

and

D

respectively are such that

PQ

touches the minor arc

EF

of this circle. Find the angle between

PB

and

QC