Two concentric circles are of radii 10 cm and 8 cm, then find the length of the chord of the larger
circle which touches the smaller circle.
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Gıven :
- Two concentric circles are of radii 10 cm and 8 cm
To Fınd :
- Length of the chord of the larger circle which touches the smaller circle.
Solutıon :
✰ As in the question We has been Given Radius of outer circle will be 10 cm that is OB and radius of inner circle will be 8 cm that is OD. We have to find the side AB So, using pythagoras theorem OD² + BD² = OB² firstly we will find the length of BD as we are already given the length of OD and OB After Finding Length of chord BD we can find Length of AB that is 2BD.
- Radius of Outer circle OB = 10cm
- Radius of inner circle OD = 8cm
In OAB,
Using pythagoras theorem
OD² + BD² = OB²
➤ (8)² + BD² = (10)²
➤ 64 + BD² = 100
➤ BD² = 100 - 64
➤ BD² = 36
➤ BD = √36
➤ BD = 6cm
Now, Finding Length of AB
➤ Length of AB = 2BD
➤ Length of AB = 2 × 6
➤ Length of AB = 12cm
∴ The length of chord is 12cm
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