Each ray starting from [math]F_1[/math] will travel, hit the ellipse at some point [math]P[/math] and reflect to [math]F_2[/math]. The distance traveled equals the sum of the distance from [math]P[/math] to [math]F_1[/math] and from [math]P[/math] to [math]F_2[/math], in other words: [math]PF_1+PF_2[/math]. By the definition of an ellipse, we have that this quantity is a constant for all points on the ellipse, no matter which path the ray takes.[br]This means the 12 rays pointing in different directions will all travel the same distance by the time they reach [math]F_2[/math]. If they are moving at the same speed, they will arrive simultaneously. Animate the diagram to see this happen.