what is the circumradius of an equilateral triangle of side 8cm
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Here ∆ ABC is an equilateral triangle.
O is the centroid of the ∆ABC.
We know that, the centroid of the the triangle is also the circumcentre for an equilateral triangle. Hence, O is the circumcentre .
Let the radius of the circle be r.
We know that in an equilateral triangle, median is also an angle bisector.
Hence, angle OBC= 1/2 angle ABC=30°.
Also , in an equilateral triangle the median is perpendicular to the base. Therefore AD_|_ BC.
∆OBD is right angled triangle.
In ∆OBD, Cos 30=adjacent / hypotenuse = BD/ r ( see figure)
Also, Cos 30 = √3/2 and BD =4
Therefore,
BD/r= 4/r = √3/2
r= 8/√3
Hence , the circumradius is 8/√3 cm.
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