Question

O is centre of the circle. Find the length of radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.

Answer 1

Let seg OP ⊥ chord AB 

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

∴l(AP) = (1/2) x 24 …[∵ l(AB) = 24 cm] 

∴ l(AP) = 12 cm …(i) 

In ∆OPA, m∠OPA = 90° 

∴ [l(AO)]² = [l(OP)]² + [l(AP)]² … [Pythagoras theorem]

∴ [l(AO)]² = (9)² + (12)² … [From (i) and l(OP) = 9 cm] 

= 81 + 144 

∴ [l(AO)]² = 225 

∴ l(AO) = √225 …[Taking square root of both sides] 

∴ l(AO) = 15 cm 

∴ The length of radius of the circle is 15 cm.