A chord of length 24 cm is at a distance of 5 cm from the centre of a circle. the radius of the circle is ___________ cm.

Correct option is A

​Given:

Chord length = 24 cm.

Distance from center to chord = 5 cm.

Formula used:

the perpendicular bisector theorem:

$$r^2 = \left(\frac{\text{Chord length}}{2}\right)^2 + \text{Distance}^2$$​​

Solution: 

By bisector theorem:

$$r^2 = \left(\frac{24}{2}\right)^2 + 5^2 \\ \ \\r^2 = 12^2 + 5^2 \\ \ \\r^2 = 144 + 25\\ \ \\ r^2 = 169 \\ \ \\ r = \sqrt{169} \\ \ \\ r = 13\ cm$$​

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