Math Is Fun Forum

... or at least for a grade 10. This is what the question states.
A semi-circle of radius 8cm, rocks back and forth along a line. The
distance between the line on which the semi-cicrle sits and a line
above the circle is 12cm. As it rocks without slipping, the
semi-circle touches the line above at two points. (When the
semi-circle hits the line above, it immediately rocks back i nthe
other direction.) The distance between the two points in millimetres
is ________.

The semicircle does not rotate around its centre of gravity but rater its center shifts as teh circle rocks form left to right. Yes i know you can figure it out by using cycloids but its grade 10.. not calculus.

Lets see is someone can proove me wrong ("THE hardest question on earth")