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

Answer 1

Autumn Armstrong

Let ABC equatorial triangle inscribed in the circle with radius r

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#

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Answer 2

Sadie Adams

The area of an equilateral triangle inscribed in a circle is given by the formula:

[ A = \frac{\sqrt{3}}{4} \times (\text{side length})^2 ]

Where the side length of the equilateral triangle is equal to the diameter of the circle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.