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,

In ΔOCB,

OB^{2 }= OC^{2} + BC^{2}

∴ BC^{2} = OB^{2} – OC^{2} = *a*^{2} – *b*^{2}

Thus, the length of chord AB is .

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