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2019 Iberoamerican Mathematical Olympiad P4

Source:

September 16, 2019

geometrytrapezoidgeometry solvedIberoamericanprojective geometryMiquel pointgeometry proposed

Problem Statement

Let

ABCD

be a trapezoid with

AB\parallel CD

and inscribed in a circumference

\Gamma

. Let

P

and

E

be two points on segment

F

(

A

,

P

,

\Gamma

,

AB

appear in that order and are distinct) such that

AP=QB

. Let

E

and

F

be the second intersection points of lines

CP

and

CQ

with

\Gamma

, respectively. Lines

AB

and

EF

intersect at

G

. Prove that line

DG

is tangent to

\Gamma

.

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