Problem reads:
Aditya is riding a bicycle on a road filled with mud patches. When it is passing through one of those patch, one of the wheels of bicycle traces part of curve $y=\sin (x)$ and the other wheel traces curve with a vertical inflection point as shown in the figure. To remove the possible effects due to the bicycle's geometry, wheel size and its tilting, take the bicycle to have vanishingly thin tires with its front axle always positioned dircetly below a vertical headset. Also, assume that its both wheels were in a mud patch when the inflection point is traversed.Determine the distance $\ell$ between its axles.
What I considered was at point of inflection the bike tyres would be in a straightline and tangential to the bottom curve which is of forward track but how to find length from it ? (I know one fact that curve of both will be sinusoidal but length part I am not able to understand how to calculate)
