Question

The length of a chord of a circle of 16.8 cm, radius is 9.1 cm. Find its distance from the centre.

Answer 1

Let CD be the chord of the Circle with centre O.

Draw seg OP ⊥ chord CD

∴ l(PD) = `(1/2) l("CD")`   …[Perpendicular drawn from the centre of a circle to its chord bisects the chord]

∴ l(PD) = `(1/2) xx 16.8`   …[l(CD) = 16.8 cm]

∴ l(PD) = 8.4 cm …(i)

∴ In ∆OPD, m∠OPD = 90°

∴ [l(OD)]² = [l(OP)]² + [l(PD)]²   ….. [Pythagoras theorem]

∴ (9.1)² = [l(OP)]² + (8.4)²    … [From (i) and l(OD) = 9.1 cm]

∴(9.1)² – (8.4)² = [l(OP)]²

∴(9.1 + 8.4) (9.1 – 8.4) = [l(OP)]²   …[∵ a² – b² = (a + b) (a – b)]

∴17.5 × (0.7) = [l(OP)]²

∴ 12.25 = [l(OP)]²

i.e., [l(OP)]² = 12.25

∴ l(OP) = `sqrt12.25`   …[Taking square root of both sides]

∴ l(OP) = 3.5 cm