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Circle and Rhombus

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Author: Annie Fetter
Description: Geometry, difficulty level 3. In the picture, we have a circle and a rhombus. BC is 6, AE is 4, angle DAE is 45 degrees, and AD is a diameter of the circle. How far is it around the perimeter of the whole figure?

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Problem page: http://mathforum.org/geopow/archive/122096.geopow.html
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