Question : The sum of the angles made by a chord XY at the centre and on the circumference of the circle is 270°. If the radius of this circle is 24 cm, then what will be the length of this chord?
Option 1: 60 cm
Option 2: 12 cm
Option 3: 36 cm
Option 4: 48 cm
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Correct Answer: 48 cm
Solution :
Given, the radius of the circle = 24 cm
Let the angle formed by the chord on the circumference be x.
Then, the angle formed by the same chord on the centre is 2x.
According to the question,
2x + x = 270°
⇒ x = 90°
It means the chord is the diameter as the diameter makes the 90° angle on the circumference.
Length of this chord = diameter = 2 × 24 = 48
Hence, the correct answer is 48 cm.
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