 Aim at This Target!  Annie Fetter
Geometry, difficulty level 4. Figure out the areas of different parts of this target, and the relation between the different areas. Can you explain this relation?
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 All Around the World  Terry Trotter & Annie Fetter
Geometry, difficulty level 2. If a wire wrapped around the equator of the Earth is lengthened by 100 meters, how far above the surface of the Earth would the wire now be if lifted off the surface an equal distance all the way around?
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 All Wet  Linda Benton
Algebra, difficulty level 3. Solve simultaneous equations, find area, and use the Pythagorean theorem and percentages to find the spraying distance needed for a circular sprinkler in a rectangular yard.
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 Another Problematic Pizza  Leigh Nataro
Trig/Calc, difficulty level 3. Find the area of a triangular piece of pizza.
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 Approximating the Circumference and Area of a Circle  Annie Fetter
Geometry, difficulty level 2. Take a circle and circumscribe a square and inscribe a square. Construct a square between the other two squares, and compare the area and the perimeter of the middle square with the area and circumference of the circle.
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 Arc to Area  Annie Fetter
Geometry, difficulty level 4. Given an arc with a measure of 40 degrees whose endpoints are at (1,5) and (5,3), find the area of the circle that contains the arc.
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 Areas of Circles in a Target  Annie Fetter
Geometry, difficulty level 2. Given one circle inside another circle. If the outer circle is 36 inches in diameter, how big must the inner circle be so that the area of the inner circle equals the area of the outer circle NOT covered by the inner circle?
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 As Far as the Eye Can See  Annie Fetter
Geometry, difficulty level 4. If I'm 5'10" tall, can I see the entire length of Lake Memphramagog, which is about 23 miles long?
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 Building a Sandbox  Leigh Nataro
Trig/Calc, difficulty level 3. Find the maximum area for a triangularshaped sandbox.
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 Building a Snow Statue  Judy Ann Brown
PreAlgebra, difficulty level 3. Determine the height of a snow statue using the given information.
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 Building a Vaulted Ceiling  Annie Fetter
Geometry, difficulty level 4. An eyebrow window is a 15inchdeep slice off an 8.5foot circle. How wide will the base of the window be?
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 Bull'seye Probability  Ethel Breuche
Algebra, difficulty level 3. Find the probability of hitting a circular target board closer to the center.
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 Center Coordinates  Leigh Nataro
Trig/Calc, difficulty level 2. Find the coordinates of the center of a circle circumscribed around a triangle.
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 A Circle Inscribed in an Isosceles Triangle  Ilmar Vitsut
Geometry, difficulty level 4. Find the radius of a circle inscribed in an isosceles triangle with sides 12, 12, and 8.
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 Circles and Tangents  Annie Fetter
Geometry, difficulty level 3. AOD is a diameter of circle O. B is any point on the circle. At B, a tangent is drawn to the circle. From the center, O, a line is drawn parallel to AB, meeting the tangent at P. Prove that PD is tangent to
the circle.
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 Circles Around  Lisa Lavelle
Math Fundamentals, difficulty level 3. Use this exploration problem to discover the relation between circumference and diameter.
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 Circumnavigating Circles  Annie Fetter
Geometry, difficulty level 3. The radii of two wheels are 10 vershoks and 5 vershoks and their centers are 30 vershoks apart. A belt goes around both of the wheels, crisscrossing between the two centers to form two internal tangents. What's the length
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 Congruent Chords and Circles  Annie Fetter
Geometry, difficulty level 4. Prove that two congruent chords in a circle are equal distances from the center of the circle.
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 Congruent Chords  Annie Fetter
Geometry, difficulty level 3. Two congruent circles are drawn, and four congruent chords are drawn, two in each circle, all perpendicular to the diameter through both circles. The distance between the two furthest chords is 20, and the distance between
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 The Corner Banking of the Daytona Speedway  Annie Fetter
Geometry, difficulty level 2. Compare the corner banking at the Daytona Speedway, which is 31 degrees, with the roof on the house and garage that I helped build.
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 Cutting the Cookie  Leigh Nataro
Trig/Calc, difficulty level 2. Where should you cut a circular cookie so its area is in a ratio of 1:2 ?
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 Dendrochronology  Annie Fetter
Geometry, difficulty level 2. Figure out about how old a large yellow birch is, given its diameter.
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 Drawing a Kite Plan  Annie Fetter
Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
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 An Eggstra Special Problem  Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of a crosssection of an egg given some dimensions of the crosssection.
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 Ellipse Areas  Leigh Nataro
Trig/Calc, difficulty level 3. Use calculus to show that the area of an ellipse is pi*a*b.
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 Equilateral Triangles and Circles  Annie Fetter
Geometry, difficulty level 2. Two vertices of an equilateral triangle are on the diameter of a circle whose area is 49 pi. The other vertex is on the circumference of the circle. What's the largest possible area of the triangle?
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 Ferris Wheel Function  Leigh Nataro
Trig/Calc, difficulty level 3. Based on given information, determine a function to describe the height above the ground of a person on a Ferris wheel as a function of time.
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 Find the Largest Equilateral Triangle  Annie Fetter
Geometry, difficulty level 3. Two vertices of an equilateral triangle lie on a diameter of a circle whose area is 36pi cm^2, and the third vertex lies on the circle. What is the largest possible area of the triangle?
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 Find the Perimeter  Annie Fetter
Geometry, difficulty level 3. In the given picture, DB and DC are both 20 inches. What's the perimeter of triangle FDG?
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 Fix This Picture  Annie Fetter
Geometry, difficulty level 2. Figure out what's wrong with this picture that includes a circle and a rhombus.
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 Football Volume  Leigh Nataro
Trig/Calc, difficulty level 3. Given the dimensions of a football, find its volume.
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 Funny Ducks  Ethel Breuche
Algebra, difficulty level 4. These funny ducks always walk exactly three feet from the lily pond. What is the area of the region bounded by their path?
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 Googol the Giant's Gargantuan Goblet  Leigh Nataro
Trig/Calc, difficulty level 2. Find the volume of Googol the Giant's elliptical paraboloid goblet.
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 Green Pastures  Carol Dormuth
Trig/Calc, difficulty level 1. Find the area of the cow's grazing pasture.
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 He Ate It All!  Mr. Marthinsen's Geometry Class
PreAlgebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza.
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 A Hexagon and a Triangle in a Circle  Annie Fetter
Geometry, difficulty level 2. A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 10 units. What is the area of the region between the
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 Intersecting Circles  Annie Fetter
Geometry, difficulty level 3. What is the maximum number of times six circles of the same size can intersect? In other words, draw six circles of the same size on a piece of paper  what is the maximum number of intersections your drawing can have?
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 It's Probably This Chord  Annie Fetter
Geometry, difficulty level 3. Find the probability that a chord of a circle will have particular
characteristics.
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 Jill and Jimmy  Soap Bubbles  Annie Fetter
Geometry, difficulty level 3. You're given two spheres with centers 14 cm apart. If the two spheres intersect in a circle whose radius is 12 cm, and the radius of one sphere is 13 cm, what's the radius of the other sphere?
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 The Length of a Belt  Annie Fetter
Geometry, difficulty level 3. The diameters of two wheels are 18 cm and 12 cm and their centers are 30 cm apart. A belt goes around them and crosses 18 cm from the center of the big wheel. How long is the belt? How do you know you're right?
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 Let's Measure the Earth  Leigh Nataro
Trig/Calc, difficulty level 3. Use Eratosthenes' measurements to calculate the radius of the earth.
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 Let the Sunshine In  Leigh Nataro
Trig/Calc, difficulty level 2. Find the dimensions of a window designed to let in the maximum amount of sunshine.
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 Magic Coins  Annie Fetter
Geometry, difficulty level 3. How come you can fit a quarter through a hole the size of a dime? Find a pair of coins in another system of money that could be used as "magic coins"  the "biggest" and "smallest" coins for which this would work.
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 Making a Six Pointed Star  Annie Fetter
Geometry, difficulty level 3. Take a circle of paper. Explain how to fold it so that you can make just one cut and get a "perfect" sixpointed star.
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 Making Pie Crust  Annie Fetter
Geometry, difficulty level 3. How would you change the recipe for a 9inch pie crust to make an 11inch pie crust?
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 A Minor Arc Subtended by a What??  Annie Fetter
Geometry, difficulty level 2. A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are radii of the circle. The length of the chord is 6 times the square root of 2. What is the length of the minor arc subtended by the chord?
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 A Minor Problem  Annie Fetter
Geometry, difficulty level 1. A chord of a circle is one side of an equilateral triangle. The other
two sides of the triangle are radii of the circle. Find the length of
the minor arc subtended by the chord, if the radius of the circle is
given.
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 More Pie, Anyone?  Annie Fetter
Geometry, difficulty level 2. How big a pie pan would you need if you made twice as much dough as you would need for a 9inch pan?
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 More Tangents!  Annie Fetter
Geometry, difficulty level 3. Given a square ABCD inscribed in a unit circle. AB is extended to P, where PC is tangent to the circle. Find the length of PD.
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 Nice Shot, Robin Hood!  Sara Aucoin, Marcie Sawyer, Pattie Draper
Trig/Calc, difficulty level 2. Answer some questions about the flight of Robin Hood's arrow.
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