Two concentric circles with centre O are of radii 3 cm and 5 cm

Circles (10)

Two concentric circles with centre O are of radii 3 cm and 5 cm. Find the length of chord AB of the larger circle which touches the smaller circle at P.

Answer

Join OA and OP

OP ⊥ AB (radius ⊥ tangent at the point of contact)

OP is the radius of smaller circle and AB is tangent at P.

AB is chord of larger circle and OP ⊥ AB

∴ AP = PB (⊥ from centre bisects the chord)

In right Δ AOP, AP2 = OA– OP2

= 52 - 32 = 16

AP = 4 cm = PB

AB = 8 cm

Exam Year: 2023