What is the area of an equilateral triangle inscribed in a circle?

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Answer 1 · 2015-11-22T21:53:28

Let ABC equatorial triangle inscribed in the circle with radius r

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Applying law of sine to the triangle OBC, we get

#a/sin60=r/sin30=>a=r*sin60/sin30=>a=sqrt3*r#

Now the area of the inscribed triangle is

#A=1/2*AM*ΒC#

Now #AM=AO+OM=r+r*sin30=3/2*r#

and #ΒC=a=sqrt3*r#

Finally

#A=1/2*(3/2*r)*(sqrt3*r)=1/4*3*sqrt3*r^2#