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in Circle : Chord and Arc by (49.4k points)
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Radius of a circle with centre O is 25 cm. Find the distance of a chord from the centre if length of the chord is 48 cm.

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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.

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