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
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Correct Answer: 24 cm
Solution :
The length of the radius is 12 cm.
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.
So, MN is the diameter.
Radius = OM = ON = 12 cm
$\therefore$ MN = 2 × (OM) = 2 × (ON) = 12 × 2 = 24 cm
Hence, the correct answer is 24 cm.
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