MathDB

Prove that three lines intersect at a point

Source: IMOC 2021 G1

August 11, 2021

geometryaltitudeantipodecyclic quadrilateral

Problem Statement

Let

\overline{BE}

and

\overline{CF}

be altitudes of triangle

ABC

, and let

D

be the antipodal point of

A

on the circumcircle of

ABC

. The lines

\overleftrightarrow{DE}

and

\overleftrightarrow{DF}

intersect

\odot(ABC)

again at

Y

and

Z

, respectively. Show that

\overleftrightarrow{YZ}

,

\overleftrightarrow{EF}

and

\overleftrightarrow{BC}

intersect at a point.

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