Q12 of 63 Page 156

In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to chord AB, then CD is equal to—

Given OA = 5 cm, AB = 8 cm and OD ⊥ AB.


We know that the perpendicular from centre of a circle to a chord bisects the chord.


⇒ AC = CB = 1/2 AB = 1/2 (8) = 4 cm


By Pythagoras Theorem,


⇒ AO2 = AC2 + OC2


⇒ 52 = 42 + OC2


⇒ 25 = 16 + OC2


⇒ OC2 = 25 – 16 = 9


⇒ OC = 3 cm


⇒ OA = OD = 5 cm [Radii of same circle]


⇒ CD = OD – OC = 5 – 3


∴ CD = 2 cm

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