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, OB2 = OM2 + BM2 $\therefore$ OM = $\sqrt{10^2-6^2}=8$ cm In $\triangle$OAM, OA2 = OM2 + AM2 $\therefore$ 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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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 : Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle which touches the smaller circle is:
Option 1: 8 cm
Option 2: 18 cm
Option 3: 10 cm
Option 4: 12 cm
Question : The radii of two concentric circles are 13 cm and 8 cm. AB is the diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and the bigger circle at E. Point A is joined to D. The length of AD is:
Option 1: 20 cm
Option 2: 19 cm
Option 3: 18 cm
Option 4: 17 cm
Question : Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E, and F. If CD = 4.5 cm, then the measure of EF is:
Option 1: 1.50 cm
Option 2: 2.25 cm
Option 3: 4.50 cm
Option 4: 9.00 cm
Question : In a circle, the length of a chord is 30 cm. The perpendicular distance of the chord from the centre of the circle is 8 cm. Find the diameter of the circle.
Option 1: 28 cm
Option 2: 34 cm
Option 3: 17 cm
Option 4: 30 cm
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