An equilateral triangle is inscribed in a circle with an area equal to 144π square cm. Find the area of a triangle.

2
by jrgmlzrte

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An equilateral triangle is inscribed in a circle with an area equal to 144π square cm. Find the area of a triangle.

2
by jrgmlzrte

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The translation of the problem is that you draw a triangle inside a circle.

The circle's area is 144 cm^2. To find the radius:

A of circle =pi* radius^2

radius=sqrt (144/pi)

r=6.77 approximately

If you connect the center point of the triangle to it's vertices you will make 3 isosceles triangles. The length of the sides of the isosceles triangle are 6.77,6.77 and the unknown side. Also, the line from the center to the vertex is an angle bisector (read properties of equilateral triangles). Since equilateral triangles have interior angles that measure 60° half of that is 30°. So the measurement of the obtuse angle of the isosceles triangle is 120°. (120°+30°+30°=180°)

To find the unknown side (length of the side of the triangle) use cosine law. I'll attach a picture of the solution.