A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?

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.