Given two points $E$ and $F$ lie on segment $AB$ and $AD$, respectively. Let the segments $BF$ and $DE$ intersects at point $C$. If it’s known that $AE+EC=AF+FC$, show that $AB+BC=AD+DC$.
Source: 2015 China South East MO Grade 11 P5
Tags: geometry
Given two points $E$ and $F$ lie on segment $AB$ and $AD$, respectively. Let the segments $BF$ and $DE$ intersects at point $C$. If it’s known that $AE+EC=AF+FC$, show that $AB+BC=AD+DC$.