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: Improved Solution by Dej Mar)

Thanks.
 
The method you describe for drawing a perpendicular is of course familiar and is the one I have always used. I suppose my point was more a reflection on the use of the word collapsible: if the compasses really do collapse when removed from the paper then you couldn’t make the two equal arcs from different points that are required in that process.

I suppose the process that is disallowed is the setting of the compasses to a definite measurement from something already drawn and then transferred for use elsewhere. Rather strange, I always think, but I suppose that without these arbitrary rules it wouldn’t be as much of a challenge.

Posted by Harry on 2010-01-13 21:03:13