SOLUTION: Good day! Can you help me with my homework? Here's the question An equilateral triangle is circumscribed about a circle of radius of 10√3 cm. What is the perimeter of the

Algebra ->  Circles -> SOLUTION: Good day! Can you help me with my homework? Here's the question An equilateral triangle is circumscribed about a circle of radius of 10√3 cm. What is the perimeter of the      Log On


   

Question 1000378: Good day! Can you help me with my homework? Here's the question
An equilateral triangle is circumscribed about a circle of radius of 10√3 cm. What is the perimeter of the triangle?

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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Good day! Can you help me with my homework? Here's the question
An equilateral triangle is circumscribed about a circle of radius of 10√3 cm. What is the perimeter of the triangle?
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Sketch the picture of the circle inside the equilateral triangle.
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Draw a radius from the center to a point of tangency.
That is a perpendicular bisector of the side of the triangle.
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Draw a line secment from the center to a vertex thus forming a right triangle.
That is a bisector of the vertex angle.
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You have a 30-60-90 degree right triangle.
The height is 10sqrt(3); the hypotenuse is 20sqrt(3)
Let the 3rd side by x
x^2 = 400*3 - 100*3
x^2 = 300*3 = 900
x = 30
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That "x" is half of a side of the triangle.
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Perimeter = 3*60 = 180 cm
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Cheers,
Stan H.
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