An equilateral triangle is inscribed in a circle of radius 18 cm. Find the length of the triangle's side.
Step by Step Explanation:
- ΔABC is inscribed in a circle. Lets O is the center of the circle.
- Now, connect all vertices of the triangle to O, and draw a perpendicular from O to 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.
= cos30° =
BD OB √3 2
BD = OB ×
= 18 ×
- Therefore, BC = 2BD = 2(9√3) = 18√3 cm
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