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The incircle of a triangle $A B C$ is tangent to $B C, C A$ and $A B$ at $D, E$ and $F$, respectively. Suppose that the incircle passes through the midpoint $X$ of $A D$. The lines $X B$ and $X C$ meet the incircle again at $Y$ and $Z$, respectively. Show that $E Y=F Z$.

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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935
Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935 Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935