An equilateral triangle ABC is inscribed in a circle centered at O and of radius 12 cm, as shown below. OD is a radius such that it is perpendicular to BC and cuts BC at point E. Then the length of OE is

4 cm

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6 cm

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8 cm

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10 cm

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Solution

The correct option is B
6 cm

Given, OD is a radius such that it is perpendicular to BC and OD = 12 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 OD and hence OE = ED = $\frac{O D}{2}$ = 6 cm.

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