Question

The diameter and a chord of a circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the centre of the circle?

Answer 1

AB is the diameter and AC is the chord.

Draw OL ⊥ AC

Since OL ⊥ AC and hence it bisects AC, O is the centre of the circle.

Therefore, OA = 10 cm and AL = 6 cm

Now, in right ΔOLA,

AO² = AL² + OL²

`=>` 10² = 6² + OL²

`=>` OL² = 100 – 36 = 64 

`=>` OL = 8 cm

Therefore, chord is at a distance of 8 cm from the centre of the circle.