Question

if a radius is circle with centre p is 25 cm the length of a chord of same circle is 48 cm find the distance of the chord from the centre p of the circle​

Answer 1

Answer:

7 cm

Step-by-step explanation:

seg OP ⊥ chord CD … [Given]

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

∴ l(PD) = (1/2) x 48 …[∵ l(CD) = 48 cm]

∴ l(PD) = 24 cm …(i) In ∆OPD, m∠OPD = 90° ∴ [l(OD)]2 = [l(OP)]2 + [l(PD)]2 … [Pythagoras theorem]

∴ (25)2 = [l(OP)]2 + (24)2 … [From (i) and l(OD) = 25 cm]

∴ (25)2 – (24)2 = [l(OP)]2

∴ (25 + 24) (25 – 24) = [l(OP)]2 …[∵ a2 – b2 = (a + b) (a – b)] ∴ 49 x 1 = [l(OP)]2

∴ [l(OP)]2 = 49 ∴ l(OP) = √49 …[Taking square root of both sides]

∴ l(OP) = 7 cm

∴The distance of the chord from the centre of the circle is 7 CM.