In a circle with centre O and the radius r cm, PQ and RS are two parallel chord of length 40 and 42 cm respectively, and the both the chords are on the same side of the O. If the distance between PQ and RS is 1 cm, the value of r is?

For parallel chords on the same side of center, distance from center to chord of length l is sqrt(r^2 - (l/2)^2). For PQ (40 cm): d1 = sqrt(r^2 - 400). For RS (42 cm): d2 = sqrt(r^2 - 441). Since chords are on same side and 1 cm apart, and RS is longer (so closer to center), d1 - d2 = 1. Solving sqrt(r^2 - 400) - sqrt(r^2 - 441) = 1 gives r = 29 cm.