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In the adjoining figure, O is the center of the circle. If OA = 5 cm, AB = 8 cm and OD ⊥ AB, then length of CD is equal to

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. 5 cm

In figure, O is the center of the circle. If OA = 5 cm, AB = 8 cm and OD ⊥ AB, then length of CD is equal to? Circle, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Circles

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Answer

Since, the perpendicular to a chord from the centre of the circle bisects the chord,

∴ AC = CB = 82\dfrac{8}{2} = 4 cm.

In right △OAC,

⇒ OA2 = OC2 + AC2

⇒ 52 = OC2 + 42

⇒ OC2 = 52 - 42

⇒ OC2 = 25 - 16

⇒ OC2 = 9

⇒ OC = 9\sqrt{9} = 3 cm.

From figure,

CD = OD - OC = 5 - 3 = 2 cm.

Hence, Option 1 is the correct option.

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