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Two concentric circles are of radii 13 cm and 5 cm. The chord of the outer circle touches the inner circle as shown in the figure. If AC = 12 cm, Find the length of the tangent BD and the chord AB

Two concentric circles are of radii 13 cm and 5 cm. The chord of the outer circle touches the inner circle as shown in the figure. If AC = 12 cm, Find the length of the tangent BD and the chord AB Correct Answer 12 cm and 24 cm

OBP

⇒ OB2 = BP2 + PO2

⇒ BP2 = OB2 – PO2

⇒ BP2 = 132 – 52

⇒ BP2 = 144

⇒ BP = √144

⇒ BP = 12 cm

⇒ BP = BD = 12 cm (∵ Tangents drawn to a circle from external point are equal)

⇒ Length of chord AB = AP + BP = 12 + 12 = 24 cm

∴ The length of tangent BD = 12 cm and chord AB = 24 cm 

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