Question : The length of a chord is 40 cm. If the angle subtended by this chord at the circumference of the circle is 90 degrees, then what will be the radius of this circle?
Option 1: 15 cm
Option 2: 25 cm
Option 3: 80 cm
Option 4: 20 cm
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Correct Answer: 20 cm
Solution : Let O be the circle's centre, and let C be the point on the circumference. Using, If an angle subtended by a chord on the circumference of a circle is 90 degrees, then the chord is the circle's diameter. ⇒ MN is the diameter. ⇒ MN = 2(OM) ⇒ 40 = 2(OM) ⇒ OM = 20 cm Hence, the correct answer is 20 cm.
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Question : The angle subtended by a chord MN on the circumference of a circle is 90 degrees. If the radius of the circle is 12 cm, then what will be the length of the chord MN?
Option 1: 30 cm
Option 2: 24 cm
Option 3: 6 cm
Option 4: 36 cm
Question : The angle subtended by a chord OP on the circumference of a circle is 90°. If the diameter of the circle is 44 cm, then what will be the length of the chord OP?
Option 1: 44 cm
Option 2: 88 cm
Option 3: 66 cm
Option 4: 22 cm
Question : A chord of length 40 cm is at a distance of 15 cm from the centre. What is the length of the chord of the same circle which is at a distance of 20 cm from the centre of the circle?
Option 3: 45 cm
Option 4: 30 cm
Question : The radius of a circle is 10 cm. What will be the angle made by a chord of length 20 cm on the circumference of this circle?
Option 1: 90°
Option 2: 120°
Option 3: 180°
Option 4: 135°
Question : The angle subtended by a chord PQ on the centre of a circle is 180°. If the length of chord PQ is 54 cm, then what will be the diameter of this circle?
Option 1: 54 cm
Option 2: 81 cm
Option 3: 27 cm
Option 4: 64 cm
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