A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
24 सेमी लंबी एक जीवा वृत्त के केंद्र पर समकोण बनाती हैं। वृत्त की त्रिज्या क्या है?
Detailed Solution & Logic
Correct Answer:
\(12\sqrt{2}\)cm/ \(12\sqrt{2}\)सेमी
Solution:
Let the radius be r.
The chord subtends a right angle ($90^\circ$) at the center.
Formula for chord length:
Chord $= 2r \sin\left(\frac{\theta}{2}\right)$
Here $\theta = 90^\circ$, so
Chord $= 2r \sin 45^\circ$
$24 = 2r \times \frac{\sqrt{2}}{2}$
$24 = r\sqrt{2}$
$r = \frac{24}{\sqrt{2}} = 12\sqrt{2}$ cm
Answer: The radius is $12\sqrt{2}$ cm.
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