In a circle of radius 13 cm, a chord is at a distance of 5cm from its center. What is the length of the chord?

It is given that the radius of the circle $$AO=OB=13cm$$

the distance of the chord from the center =5cm,

We know that the minimum distance of a line from a point is always perpendicular to the line.

Now applying the Pythagoras theorem,

$$AO^2=AD^2+DO^2$$

Now, substituting the values,

$$AD^2=AO^2-OD^2=13^2-5^2$$

taking the square root of both side,

$$AD=\sqrt{144}=12$$cm

As we know, from the rule of circle

The perpendicular from the center to the chord, always bisect the chord,

Hence, the length of the chord $$AB=2\times AD=2\times12=24$$cm