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
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