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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