Let L and N be adjacent cusps of a cycloid.
Let P be a point on the cycloid between L and N.

Construct with straightedge and compass the tangent line to the cycloid at point P.

(In reply to Re: Solution (Harry) (spoiler) by Kenny M)

Having had the advantage of being a reviewer of this problem, not knowing the solution, and having an interest in cycloids (a problem proposed at a similar but withdrawn) I did research this and found the same link:
http://www.ies.co.jp/math/java/calc/cycle_ang/cycle_ang.html

It seemed on Day1 there was a lack of interest, so in light of the above I proposed the comment with hope for some enticement for a solution for Bractals. 

With prior knowledge (and being naive at that point) it would have been morally wrong to propose such a solution.

Posted by brianjn on 2010-01-12 08:34:10