Can the length of any chord that is parallel to the bases of a trapezoid be found if the lengths of the two bases are known?
Given the length of the bases of a trapezoid, the median can be found by the formula (b1 + b2)/2. From this the median can be found of the two resultant trapezoids formed by the median and the bases, and ad infinitum. So, at least theoretically, the length of any chord that is parallel to the bases can be found. I wonder if there is anyone who has reduced this iterative process into a formula.
This seems more suited to a general math forum like "math stack exchange" than to Ask Sage.
The answer is simple though: the length of a parallel to the bases varies linearly with the height.
So the length is
(1 - t) * b1 + t * b2at a fractiontof the way from base 1 to base 2.See intercept theorem.