MathDB

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.

G1