If Radii of two concentric circles are 15cm and 17cm , then the length of each chord of one circle which is tangent to other is:a) 8cm b) 16cm c) 30cm d) 17cmplease explain me !
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then consider 2 concentric circles with 17and 15cm of radii. so here only one chord of the bigger circle is possible which is tangent to the smaller circle. so consider the Pythagoras theorem. so let ,
17cm be the hypotenuse, and 15cm be the perpendicular to the chord of the bigger circle. so the length of the chord=289-225=√64=8cm= 2×8cm.
see here we are applying Pythagoras theorem.and since the perpendicular of a circle to a chord always bisects it, so we have multiplied it by 2.
17cm be the hypotenuse, and 15cm be the perpendicular to the chord of the bigger circle. so the length of the chord=289-225=√64=8cm= 2×8cm.
see here we are applying Pythagoras theorem.and since the perpendicular of a circle to a chord always bisects it, so we have multiplied it by 2.
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Answer:
16 cm
Step-by-step explanation:
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,
= +
= +
289 = 225 +
289 - 225 =
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.
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