Originally Posted by
Unknown008
It's ok, I think I can give you a greenie now, had spread the rep enough times... let's try.
30. Finally the last one!
A trapezium ABCD has AD and BC parallel and a point E is chosen on the base AD so that the line segments BE and CE divide the trapezium into three right-angled triangles. These three right-angled triangles are similar, but no two are congruent. In common units, all the triangles' sides lengths are integers. The length of AD is 2009. What is the length of BC?
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Here, my drawing tells me that if the angle BEC is 90, and AB is a slant, then ABE must be 90 too. However, that means that AB and EC are parallel, and therefore the triangles ABE and BCE are congruent. However, if that were a rectangle, then, that would solve matters. Is that right?