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Mathematics

Given O is center of the circle with chord AB = 8 cm, OA = 5 cm and OD ⊥ AB. The length of CD is :

A chord of length 6 cm is drawn in a circle of diameter 10 cm, its distance from the center of the circle is : Circle, Concise Mathematics Solutions ICSE Class 9.

  1. 3 cm

  2. 5 cm

  3. 2 cm

  4. none of these

Circles

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Answer

Given, the length of chord AB = 8 cm.

OD ⊥ AB.

Since, perpendicular drawn from the center of a circle to a chord bisects it.

∴ OC bisects AB.

⇒ AC = AB2=82\dfrac{AB}{2} = \dfrac{8}{2} = 4 cm

Radius of the circle, OA = 5 cm.

In Δ OAC, ∠C = 90°

Using Pythagoras theorem,

∴ OA2 = OC2 + AC2

⇒ 52 = OC2 + 42

⇒ 25 = OC2 + 16

⇒ OC2 = 25 - 16

⇒ OC2 = 9

⇒ OC = 9\sqrt{9}

⇒ OC = 3 cm

Since, OD = OA (Radii of the circle)

From figure,

⇒ CD = OD - OC = 5 - 3 = 2 cm.

Hence, option 3 is the correct option.

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