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 = 7 cm, then the radius of this circle is

22 cm

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18 cm

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14 cm

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10 cm

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Solution

The correct option is C
14 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 = 7 cm.

Therefore OE = OD + DE = 7 cm + 7 cm = 14 cm

Hence radius of this circle is 14 cm.

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