Consider a string P of length l that is laid out as a straight-line segment.…

GATE · 2026 · BM · General AptitudeGATE · 2026 · CE · Set 2 · General AptitudeGATE · 2026 · ME · General AptitudeGATE · 2026 · MT · General Aptitude

Consider a string P of length l that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length x they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of x/l is __________

String K as a semicircle over diameter string P, then both shortened and rearranged as a circle and diameter.

A.
$\pi$
B.
$\frac{\pi-1}{2\pi}$
C.
$\frac{\pi}{2(\pi-1)}$
D.
$\frac{\pi}{\pi-1}$

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