Question : The radii of two concentric circles are 34 cm and 50 cm. A and D are the points on a larger circle and B and C are the points on a smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?
Option 1: 60 cm
Option 2: 80 cm
Option 3: 75 cm
Option 4: 40 cm

Question

Question : The radius of the two concentric circles are 17 cm and 10 cm. A straight line ABCD intersects the larger circle at points A and D and intersects the smaller circle at points B and C. If BC = 12 cm, then the length of AD(in cm) is:
Option 1: 20
Option 2: 24
Option 3: 30
Option 4: 34

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Answer 1

Correct Answer: 80 cm

Solution :
Given: Radius $O A = 50$ cm
$O B = 34$ cm
$B E = \frac{B C}{2} = \frac{32}{2} = 16$
Now, in $△ O B E$
$O E^{2} = O B^{2} - B E^{2}$
$\Rightarrow O E^{2} = 34^{2} - 16^{2}$
$\Rightarrow O E^{2} = 1156 - 256 = 900$
$∴ O E = 30$
In $△ O A E$
$A E^{2} = O A^{2} - O E^{2}$
$\Rightarrow A E^{2} = 50^{2} - 30^{2}$
$\Rightarrow A E^{2} = 2500 - 900 = 1600$
$∴ A E = 40$
$∴ A D = A E \times 2 = 40 \times 2 = 80$
Hence, the correct answer is 80 cm.

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Question : The radii of two concentric circles are 34 cm and 50 cm. A and D are the points on a larger circle and B and C are the points on a smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?Option 1: 60 cmOption 2: 80 cmOption 3: 75 cmOption 4: 40 cm

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Question : The radii of two concentric circles are 34 cm and 50 cm. A and D are the points on a larger circle and B and C are the points on a smaller circle. If ABCD is a straight line and BC = 32 cm, then what is the length of AD?
Option 1: 60 cm
Option 2: 80 cm
Option 3: 75 cm
Option 4: 40 cm