The line has equation Ax+By+C=0
You can change line parameters and observe its location relative to the coupler curve.
You can also press teh F button to see the coordinates of the coupler point F.
This mechanism generates sinusoidal motion.
Imagine a pen at F tracing on paper moving from left to right at velocity v.
What parameter do you need to change to alter the amplitude of the curve?
How about the period?
The problem – find the triangle with minimal perimeter that can be inscribed in a given triangle.
The solution: reflection helps reduce the problem to a single parameter.
The answer: is geometrically appealing.
Can you solve it without using the hint?
We use a trick to let the trace "open up" as you drag a point.
The trick is this: an initial point is given parametric location s*t, create a tangent at this point and its envelope as s varies.
Now hide the original point and create another point with parameter t, and make it draggable.
Dragging the new point changes the value of t and we see a trace from 0 to t.