A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord

Answer Details

To find the length of the chord, we can use the Pythagorean theorem.

First, we can find the radius of the circle, which is half of the diameter:

radius = 26cm / 2 = 13cm

The chord divides the circle into two parts, each with its own radius, as shown below:

    O
   / \
  /   \
 /     \
--------  
  R    R 

We can draw a line from the center of the circle to the midpoint of the chord, which will bisect the chord and form a right angle with the chord:

    O
   / \
  /   \
 /  .  \
--------  
  R    R 

The line from the center of the circle to the midpoint of the chord is also the perpendicular bisector of the chord, and so it divides the chord into two equal segments.

Let the length of each of these segments be x. Then, we can use the Pythagorean theorem to find x:

x^2 + 5^2 = 13^2
x^2 = 169 - 25
x^2 = 144
x = 12

Therefore, the length of the chord is twice the length of one of the segments:

length of chord = 2x = 2(12) = 24 cm

So the correct option is (c) 24cm.