Question

C is the centre of the circle whose radius is 10 cm. Find the distance of the chord from the centre if the length of the chord is 12 cm.

Answer 1

l(AC) = 10 cm

l (AB) = 12 cm

seg. CD ⊥chord AB

The perpendicular drawn from the centre of the circle to its chord bisects the chord.

∴ `l ("AD") = 1/2 l("AB")`

= `1/2 xx 12`

= 6 cm

In Δ ACD,
We apply the Pythagoras theorem

CD² + AD² = AC²

⇒ CD² + 6² = 10²

⇒ CD² + 36 = 100

⇒ CD² = 100 − 36

⇒ CD² = 64

⇒ CD = 8 cm 

Thus, the distance of the chord from the centre is 8 cm.