The lengths of two p

Case I. When the two chords are on the same side of the centre
                                                                                                     
Given: OM ⊥ AB
∴ M is the mid-point of AB.      (∵ The perpendicular from the centre of a circle to a chord bisects the chord) 
         BM = AM = AB = (6) = 3 cm
Given: ON ⊥ CD
∴ N is the mid-point of CD.       (∵ The perpendicular from the centre of a circle to a chord bisects the chord)  
∴ DN = CN = CD = (8) = 4 cm
  In right triangle OMB,
  OB² = OM² + MB²                          ( By Pythagoras Theorem )
         = (4)² + (3)²
         = 16 + 9 = 25
     ⇒ OB = = 5 cm
           ∴ OD = OB = 5 cm                   ( Radii of a circle)
In right triangle OND,
           OD² = ON² + ND²                      (By Pythagoras Theorem)
            ⇒ (5)² = ON² + (4)²
            ⇒ 25 = ON²+16
            ⇒ ON² = 25-16
            ⇒ ON² = 9
            ⇒ ON = = 3 cm
Hence the distance of the other chord from the centre is 3 cm.
Case II. When the two chords are on the opposite sides of the centre                                                As in case I
ON = 3 cm.