Question

If radii of two concentric circles are 15cm and 17 cm, then length of each chord of one circle which is tangent to another is?

Answer 1

answer AB is 16........

Answer 2

O be the center of circles.
AB be the chord to the larger circle and tangent to smaller circle at P.
OP be radius of smaller circle i.e., OP = 15 cm
OA & OB be radius of larger circle i.e., OA = OB = 17 cm
 now, 
OP ⊥ AB ( radius and tangent of a circle are ⊥ to each other)
∴ In ΔOAP by PGT,
$OA^{2}$ = $OP^{2}$ + $AP^{2}$
$17^{2}$ = $15^{2}$ + $AP^{2}$
289 = 225 + $AP^{2}$
289 - 225 = $AP^{2}$
64 = $AP^{2}$
$\sqrt{64}$ = AP
AP = 8 cm.
Now,
In ΔOAP & ΔOPB
OA = OB = 17 cm (Radii of same circle)
OP = OP (Common Side)
∠OPA = ∠OPB = 90° ( OP⊥AB)
∴ ΔOAP ≡ ΔOPB (By R.H.S axiom)
∴ AP = PB by C.P.C.T
Now, 
AB = AP + PB
AB = 2 x AP
AB = 2 x 8 cm
AB = 16 cm
∴ Length of Chord is 16 cm.

Hope you like my answer.