Question

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

Answer 1

Step 1:

The radius r is half the diameter.

`r = "diameter"/2`

r = `26/2`

= 13 cm

Step 2:

Let x be half the chord length.

The radius, the distance from the center to the chord and half the chord form a right-angled triangle.

r² = (distance)² + x²

13² = 5² + x²

169 = 25 + x²

x² = 169 – 25

x² = 144

x = `sqrt(144)`

= 12 cm

Step 3:

The full chord length is 2x.

Chord length = 2 × 12 = 24 cm

The length of the chord is 24 cm.