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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