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 = a2 – b2
Thus, the length of chord AB is .