Question : Half of the length of a chord of a circle is 12 cm and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
Option 1: 12 cm
Option 2: 13 cm
Option 3: 10 cm
Option 4: 24 cm
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Correct Answer: 13 cm
Solution : Here, the radius of the circle is OA. AD is half the length of the chord, AB. AD = 12 cm OD = 5 cm Using Pythagoras theorem we get, OA2 = OD2 + AD2 ⇒ OA = $\sqrt{5^2+12^2}=13$ cm Hence, the correct answer is 13 cm.
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Question : A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. The radius of the circle is:
Option 1: 13 cm
Option 2: 12 cm
Option 3: 16 cm
Option 4: 15 cm
Question : The length of the chord of a circle is 8 cm and the perpendicular distance between the centre and the chord is 3 cm, then the diameter of the circle is equal to:
Option 1: 5 cm
Option 2: 10 cm
Option 3: 3 cm
Option 4: 7 cm
Question : A circle of radius 5 cm and the length of tangent drawn from a point $X$ outside the circle is 12 cm. The distance of the point $X$ from the centre of the circle is:
Option 2: 11 cm
Option 4: 13 cm
Question : The radius of a circle is 10 cm. The distance of chord PQ from the centre is 8 cm. What is the length of chord PQ?
Option 1: 16 cm
Option 2: 15 cm
Option 3: 12 cm
Option 4: 14 cm
Question : A chord is drawn in a circle of radius 10 cm, if the distance of the chord from the centre is 6 cm, then the length of the chord (in cm) is:
Option 1: 10
Option 2: 12
Option 3: 16
Option 4: 8
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