In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is
(a) 8 cm (b) 14 cm (c) 16 cm (d) √136 cm
Let the two concentric circles with centre O.
AB be the chord of the larger circle which touches the smaller circle at point P.
∴ AB is tangent to the smaller circle to the point P.
⇒OP⊥AB
By Pythagoras theorem in ΔOPA,
OA2=AP2+OP2
⇒102=AP2+62
⇒AP2=100−36=64
⇒AP=8
In ΔOPA,
Since OP⊥AB,
AP = PB (∵ Perpendicular from the centre of the circle bisects the chord)
AB=2AP=2×8=16 cm
∴ The length of the chord of the larger circle is 16 cm.