Two parallel chords AB and CD of a circle are of lengths 60 cm and 80 cm respectively. They are on the same side of the centre O and 10 cm apart. What is the diameter of the circle?

Let r be radius. Distance from center to 80-chord: √(r²−1600). To 60-chord: √(r²−900). Difference = 10. √(r²−900) − √(r²−1600) = 10. Solving: let u = √(r²−900), v = √(r²−1600). u−v=10, u²−v² = 700, so u+v = 70, u = 40, v = 30. r² = 900+1600 = 2500, r = 50. Diameter = 100 cm.