An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 2.2 cm, then the diameter of this circle is

9.6 cm

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9.2 cm

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8.8 cm

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8.4 cm

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Solution

The correct option is C
8.8 cm

We know that a side of an equilateral triangle drawn with vertices on a circle bisects the radius perpendicular to it.

So, the side BC of equilateral triangle ABC bisects the radius OE and hence OD = DE.

Given, OD = 2.2 cm.

Therefore OE = OD + DE = 2.2 cm + 2.2 cm = 4.4 cm

Hence length of the diameter of this circle is 8.8 cm. [diameter = 2 $\times$ radius]

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