An equilateral triangle with a side of length 6√3 cm is inscribed in a circle. Find the radius of the circle.
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Step by Step Explanation:
- ΔABC is inscribed in a circle. Let O be the center of the circle.
- Now, connect all vertices of the triangle to O, and draw a perpendicular from O meet the side BC of the triangle at point D.
- We know, all the angles of an equilateral triangle measure 60°.
So, angle ACB = ABC = CBA = 60°
OB and OC are bisectors of ∠B and ∠C respectively,
∠OBD = 30°
- Since, triangle ODB is a right- angled triangle.
= cos 30° =
= 6 cm
- Therefore, the radius of the circle is 6 cm.