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June 24th, 2011, 09:06 PM   #1
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Finding Sides and area of trapezoid around two circles.

Find Sides and area of trapezoid around two circles with radius=1 and Radius=3.
Here is the exact picture give by teacher (not drawn to scale)

That was the only info given. Any guidance or suggestions on how to solve?
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June 24th, 2011, 10:57 PM   #2
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Assume the circles are externally tangent and the trapezoid is isosceles.
The sides are and The area is
I'm 99% certain that my answers are correct.
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June 25th, 2011, 07:58 AM   #3
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Re: Finding Sides and area of trapezoid around two circles.

Orienting the trapezoid so the r = 3 circle is at the bottom and assuming the centers of the circles are in a line perpendicular to the base of the trapezoid, the angle in the bottom two corners is arctan(2) and the height of the trapezoid is 8.
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June 25th, 2011, 09:46 AM   #4
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Re: Finding Sides and area of trapezoid around two circles.

Where did you get the number 2 from?
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June 25th, 2011, 01:40 PM   #5
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Re: Finding Sides and area of trapezoid around two circles.

From a mistake, sorry about that.
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June 25th, 2011, 03:40 PM   #6
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Re: Finding Sides and area of trapezoid around two circles.

im still confused. how would i find the area of the trapezoid though?
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June 25th, 2011, 04:22 PM   #7
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Height 8 with bases and therefore area
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June 25th, 2011, 05:18 PM   #8
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Re: Finding Sides and area of trapezoid around two circles.

Why can't the picture be drawn like this? Then the area is 30+16 sqrt(3)
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June 25th, 2011, 07:42 PM   #9
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Re: Finding Sides and area of trapezoid around two circles.

How did you find the length of the sides?
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June 25th, 2011, 08:12 PM   #10
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Re: Finding Sides and area of trapezoid around two circles.

Quote:
Originally Posted by Spaghett
How did you find the length of the sides?
From the centers of the circles, draw all the radii to the points of tangency. With r=1 and R=3 you should get lots of 30-60-90 triangles (probably similar to the method that johnny used). The height of the trapezoid (the way I drew it) is .
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