Let O be the center of circle. Draw two concentric circles are of radii 6.5 cm and 2.5 cm, and
AB = Chord of the larger circle which touches the smaller circle at C.
From Figure:
OC = radius = 2.5 cm
OA = 6.5 cm
AC = CB
OC ⊥ AB and OC bisects AB at C.
In right ∆OPT,
By Pythagoras Theorem:
OA2 = OC2 + AC2
6.52 = 2.52 + AC2
42.25 = 6.25 + AC2
AC = 6
Length of chord of a circle = AB = 2 x AC = 2 x 6 = 12 cm.