Lord El-Melloi II-sei no Jikenbo - Vol. 1 Ch. 4

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I understood the explanation but there is a key fact still missing. The lines from the constellations/angel rooms to the intersection are completely arbitrary. The line from Michael's room passes through the center of the semicircle but the other two make no sense. The point where they intersect should obviously be the center of the semicircle. Where do the lines from Ariel and Mihael come from?
 
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Meeting in the middle would assume the angels were assigned based off the angle of the door of the room and they arent.

The angles of all Angels revealed (ch 3 has the ones for the other members) run between 210 to 240.

These on a north justified compass all would be located in the south west and would originate from a point originating in the northeast.

Since El Melloi's room has the flattest Angle I'm forced to assume North is 0 and West is 270 on this map.

If you were to follow the angle from the door of his room on the map you would need to give an angle (and be assigned an angel) between 270 and 360 in which case yes you would meet in the middle.
 

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