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 = 5 cm, then the radius of this circle is

15 cm

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12 cm

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10 cm

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7 cm

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Solution

The correct option is C
10 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 = 5 cm.

Therefore OE = OD + DE = 5 cm + 5 cm = 10 cm

Hence radius of this circle is 10 cm.

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