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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Correct Answer: 30
Solution :
Given:
OB = 10 cm, OA = 17 cm, BC = 12 cm
Drawing a perpendicular from centre O on BC cuts BC in M.
BM = $\frac{1}{2}×$BC = $\frac{1}{2}×$12= 6 cm
From $\triangle$OBM,
OB
2
= OM
2
+ BM
2
$\therefore$ OM = $\sqrt{10^2-6^2}=8$ cm
In $\triangle$OAM,
OA
2
= OM
2
+ AM
2
$\therefore$ AM = $\sqrt{17^2-8^2}=15$ cm
AD = 2 × AM = 2 × 15 = 30 cm
Hence, the correct answer is 30 cm.
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