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

Let seg AB be the chord of the circle with centre C. 

Draw seg CD ⊥ chord AB.

∴ l(AD) = (1/2) l(AB) …[Perpendicular drawn from the centre of a circle to its chord bisects the chord] 

= (1/2) x 12 …[∵ l(AB) = 12 cm] 

∴ l(AD) = 6 cm …(i) 

∴ In ∆ACD, m∠ADC = 90° 

∴ [l(AC)]² = [l(AD)]² + [l(CD)]² … [Pythagoras theorem] 

∴ (10)² = (6)² + [l(CD)]² … [From (i) and l(AC) = 10 cm] 

∴ (10)² – (6)² = [l(CD)]² 

∴ 100 – 36 = [l(CD)]² 

∴ 64 = [l(CD)]² 

i.e.[l(CD)]² = 64 

∴ l(CD) = √64 …[Taking square root of both sides] 

∴ l(CD) = 8 cm 

∴ The distance of the chord from the centre of the circle is 8 cm.