A 8 cm long perpendicular is drawn from the centre of a

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A 8 cm long perpendicular is drawn from the centre of a circle to a 12 cm long chord. The diameter of the circle is :

1. 10 cm.
2. 12 cm.
3. 16 cm.
4. 20 cm.

Correct Option: D

According to question , we draw a figure of a circle with centre O ,

Given that , AB = Length of chord = 12 cm.
OC ⊥ AB
∴ AC = CB = 6 cm.
OC = 8 cm.
In ∆ OAC,
OA = √OC² + CA²
OA = √8² + 6²
OA= √64 + 36 = √100 = 10 cm.
∴ Diametre of circle = 2 × OA = 2 × 10 = 20 cm.