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?

2
thanks
the formula is that if you are given the distance of the chord from the center you can and you know the radius of that circle you can find it
once these people stop writing I would be able to help with a diagram
8*2=16 because perpendicular from centre bisects the chords
i understood thanks

Answers

2016-01-20T21:23:28+05:30
2016-01-20T21:33:18+05:30
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.

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