Question

1. Two concentric circles are of radii 6om and
10cm. Find the length of the chord of the larger
circle which touches the smaller circle.3 m answer please it's urgent​

Answer 1

Answer:

concentric circles are of radii 6om and

10cm. Find the length of the chord of the larger

circle which touches the smaller circle.3 m answer please it's urgent

Answer 2

Let the two concentric circles have the centre O and let AB be the chord of an outer circle whose length is D and which will also be tangent to the inner circle at point D because it is given that the chord touches the inner circle.

The radius of inner circle OD = 6 cm and the radius of outer circle OB = 10 cm In ΔOAB

⇒ OA = OB …radius of outer circle

Hence

ΔOAB is isosceles triangle

As radius is perpendicular to tangent OC is perpendicular to AB OC is altitude from apex and in isosceles triangle the altitude is also the median

Hence

AD = DB

Hence

AB = 2DB

Consider ΔODB

⇒ ∠ODB = 90° …radius perpendicular to tangent

Using Pythagoras theorem

⇒ OD2 + BD2 = OB2

⇒ 62 + BD2 = 102

⇒ 36 + BD2 = 100

⇒ BD2 = 100 – 36

⇒ BD2 = 64

⇒ BD = ±8 As length cannot be negative

⇒ BD = 8 cm

⇒ AB = 2 × 8

…since AB = 2BD

⇒ AB = 16 cm

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