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 = OA² – OP²

= 5² - 3² = 16

AP = 4 cm = PB

AB = 8 cm

• Exam Year: 2023