Question

A chord of length 10 cm is drawn in a circle of diameter 26 cm. Find its distance from the centre of the circle.

Answer 1

Given:

Chord length AB = 10 cm

Diameter = 26 cm

Radius OA = `26/2` = 13 cm

Step-wise calculation:

1. Draw OM ⟂ AB,

So, M is the midpoint of AB. 

Hence, `AM = (AB)/2`

= `10/2`

= 5 cm

2. In right triangle OAM,

Apply Pythagoras:

OM² = OA² – AM² 

= 13² – 5² 

= 169 – 25

= 144

Therefore, `OM = sqrt(144)`

= 12 cm

The distance from the centre of the circle to the chord is 12 cm.