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 = 3 cm, then the diameter of this circle is
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 OE and hence OD = DE.
Given, OD = 3 cm.
Therefore OE = OD + DE = 3 cm + 3 cm = 6 cm
Hence length of the diameter of this circle is 12 cm. [diameter = 2 × radius]