Two Concentric Circles of radii A and B ( A>B) are given. the Chord AB of larger circle touches the smaller circle at C. The length of AB is

Let O be the centre of the concentric circles. AB is the chord of the larger circle and tangent to the smaller circle at C.

Given, OC = b and OB = a.

AB is the tangent to the smaller circle.

∴ ∠OCB = 90°     (Radius is perpendicular to the tangent at point of contact)

OD ⊥ AB,


OB2 = OC2 + BC2

∴ BC2 = OB2 – OC2 = a2b2

Thus, the length of chord AB is .

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