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Geometry Problem 1181: Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter

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Some geometric shapes have the curious property that their area and perimeter are equal. For example, in the diagram above, the L-shape has an area of 26 square units and a perimeter of 26 linear units. In fact, if you choose the scale...

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Some geometric shapes have the curious property that their surface areas and volumes are equal. For example, the diagram above shows a cylinder of radius 3 and height 3 capped by a hemisphere of radius This solid has a surface area...