Question

In the given figure, if OA = 5cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to _______.

Answer 1

Given:
OA = 5cm ...(1)
AB = 8 cm
OD is perpendicular to AB


We know, perpendicular from the centre to the chord bisects the chord.
Therefore, AC = CB = $\frac{1}{2}AB$
⇒ AC = 4 cm ...(2)


In right angled ∆OAC,
Using pythagoras theorem
OA² = AC² + OC²
⇒ 5² = 4² + OC² (From (1) and (2))
⇒ 25 = 16 + OC²
⇒ OC² = 25 − 16
⇒ OC² = 9
⇒ OC = 3 cm


OD = 5 cm (radius)
∴ CD = OD − OC
⇒ CD = 5 − 3
⇒ CD = 2 cm

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Hence, CD is equal to 2 cm.