# Crossed Line Segments

Geometry Level 3

Line segments $$AB$$ and $$CD$$ intersect (internally) at point $$E$$. We are given that $$AE=20$$, $$EB= 12$$, $$CE=10$$ and $$ED = 24$$. What are the last 3 digits of the expression $$AC \times BD + BC \times AD$$?

Details and assumptions

If you think that the last 3 digits are 012, then you can enter either 12 or 012 as your numerical answer.

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