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 Additional investigations Dalmatian Day: Cut various circles from paper measuring 9 inches by 12 inches. What's the area of the circles and the percent of paper wasted after cutting out the circles? Target Areas: Determine the area of a target formed by concentric circles. Inscribed Circle: Finding an estimation for the area of a circle. Summing Circles: Finding the cumulative area of shrinking circles. Dividing Pizza: Compare slices of pizza from pizzas with different diameters. Segment Areas: Determine the measure of the central angle of a circle that will make the shaded region's area 1/ 4 of the entire circle's area. Circle Inscribed in a Semicircle: Compare attributes of a circle that is inscribed in a semicircle to attributes of that semicircle. Surrounding Squares: Find a method that will construct a square that has the same area as the area of a given circle. Surface Area: Relate the surface area of a sphere to the area of a circle. Walking Around the World: Compare the distance a man's head travels to the distance his feet travel when he walks around the world. Wrapping Around the World: How much string is needed to wrap around the world? N-Sided Circle?: Compare the perimeters of polygons to the circumference of a circle. Rationalize Pi: Approximate pi with a rational number. A Common Ratio: Compare the ratio of the circumference (C) and the diameter (d) of several circles. Running in Circles: Can Peanut the dog get a drink of water if his bowl of water is 20 feet away from the stake he is tied to? The Bicycle Problem: Compare the radius of a bicycle wheel to the number of revolutions the wheel makes. Grazing for Mooey: How many square meters of grazing ground does Mooey the cow have? Squaring the Circumference: Find a method that will construct a square that has the same perimeter as the circumference of a given circle. Opposite Angles: Find a relationship between the opposite angles in a quadrilateral inscribed in a circle. Inscribed in a Semi-Circle: Examine the angles inscribed in a semicircle. Inscribed in a Triangle: Construct a circle inscribed in a triangle so that it will always remain inscribed in the triangle. Perpendicular Bisectors: Describe the significance of the perpendicular bisectors of two segments that have endpoints on a given circle. Passing thru the Center: What is the relationship between two circles relate that pass through each other's centers? Equidistant Chords: Determine the relationship between two segments that have endpoints on a circle if the segments are the same perpendicular distance away from the center of the circle. Quarter-Circle Spiral: What relationships can you find between the radii of quarter circles? Inscribed Parallelogram: What must be true about a parallelogram that is inscribed in a circle? Locus of Reflection: Trace the path of a reflected point to determine a pattern and the reason the pattern occurs. Packing Circles: Investigate how many circles you can pack inside a square. Tangent Lines to a Circle: How does a tangent line relate to the radius that intersects the tangent line? Wheeling Along: Determine the number of times a smaller wheel must revolve before a larger wheel begins rolling if the wheels will eventually meet under certain conditions. Pizza Pizzazz: Thomas complains the prices of pizzas at a restaurant are unfair. Why? Submit your idea for an investigation to InterMath.