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MathNet 2014 Question 24

Math Olympiad Vault · MathNet 2014

Question 24

On the circumference of a circle, 6 points $A$, $B$, $C$, $D$, $E$, $F$ are placed in this order counter-clockwise, and three lines $AD$, $BE$ and $CF$ intersect at a single point. If
$$
AB = 1,\ BC = 2,\ CD = 3,\ DE = 4,\ EF = 5,
$$
find the value of $FA$. Here we denote the length of a line segment $XY$ also by $XY$.

Question illustration