SOLUTION: Find the area of an equilateral triangle whose vertices lie on a circle with radius 2cm.

Question 18511: Find the area of an equilateral triangle whose vertices lie on a circle with radius 2cm.
Answer by tran3209(100) (Show Source): You can put this solution on YOUR website!
Let ABC be the equilateral triangle whose verticle lie on the circle with a radius of 2cm and "O" as the center.
AH the perpendicular from A to BC is the altitude
In an equilateral triangle the altitude is also the median.
So O is also the centroid of the triangle
So ---->OH/AO = �

OH= OA/2 = 2/2 = 1cm
AH=2+1=3cm
In the triange OCH
OC=2cm

OH=1cm
apply the pythagorean theorem
OC^2= OH^2 + HC^2
or
HC^2 =OC^2 - OH^2
=2^2-1^2
=4-1=3
HC = √3
The side of the triangle BC =2HC = 2√3
The area of the triangle:
AH X BC
-------
2
= 2 X 2√3
--------
2
= 4√3
-----
2
Area of the triangle is 2√3 cm^2

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