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parmenides51 wrote: Given a rectangle $ABCD$, which is located on the line $\ell$. They want to "invert" it by first rotating around the vertex $D$, and then rotating around the vertex $C$ (see figure). Why is the length of the line by which vertex $A$ moves at such movement, if $AB = 30$ cm, $BC = 40$ cm? (Alexey Panasenko) Could you please check the problem again?

Quote: Given a rectangle $ABCD$, which is located on the line $\ell$. They want to "invert" it by first rotating around the vertex $D$, and then rotating around the vertex $C$ (see figure). Why is the length of the line by which vertex $A$ moves at such movement, if $AB = 30$ cm, $BC = 40$ cm? Here is a better translation: Quote: Given a rectangle $ABCD$, which is located on the line $\ell$ They want it "turn over" by first turning around the vertex $D$, and then as point $C$ appears on the line $\ell$ - by making a turn around the vertex $C$ (see figure). What is the length of the curve along which the vertex $A$ is moving, at such movement, if $AB = 30$ cm, $BC = 40$ cm?