If two concentric circles are of radii 5 cm and 3 cm, then the length of the chord of the larger circle which touches the smaller circle is

Explanation

Given : C1 and C2 be the two concentric circles having radius r1 = 3 cm and r2 = 5 cm respectively. To find : AB = ? Solution : AB is the the tangent to the circle C1 , hence ∠ OPB = 90∘ Also, the perpendicular from the centre of a circle to a chord bisects the chord. Thus, in △ OPB, => (P B)2 = (OB)2 − (OP )2 => (P B)2 = (5)2 − (3)2 => (P B)2 = 25 − 9 = 16 16 (10) => P B = 16 = 4 cm ∴ AB = 2 × 4 = 8 cm => Ans - (D)