Problems of the Week


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      Title Subject Grade
    A Carpenters Trisection
    Explain whether or not the given method of trisecting an angle, using only a carpenter's square, really works.
    Geometry 6th to 8th, High School
    A Circle Inscribed in an Isosceles Triangle
    Find the radius of a circle inscribed in an isosceles triangle with the given side lengths.
    Geometry 6th to 8th, High School
    A Gardening Puzzle
    If a rectangular garden were 2 feet wider and 3 feet longer, it would be 64 square feet larger. If it were 3 feet wider and 2 feet longer, it would be 68 square feet larger. What are the dimensions of the garden?
    Geometry 6th to 8th, High School
    A Line of Reflection
    Find the equation of the line of reflection for triangle ABC and its image, A'B'C'.
    Geometry 6th to 8th, High School
    A Minor Problem
    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.
    Geometry 6th to 8th, High School
    A Parallelogram Dissection
    Cut the given parallelogram along the dotted lines and rearrange the three resulting triangles to form what seems to be a square. What needs to be true of the original figure in order for the resulting figure to actually be a square?
    Geometry 6th to 8th, High School
    A Picturesque Pythgorean Proof
    Write a proof to go with this picture.
    Geometry 6th to 8th, High School
    A Quickie Triangle Puzzle
    Find the length of the unknown side of this triangle using knowledge of special right triangles.
    Geometry 6th to 8th, High School
    A Rectangle Dissection
    Cut the given rectangle into three pieces as indicated by the dashed lines. Rearrange the pieces to form a square, and explain why the resulting shape actually is a square.
    Geometry 6th to 8th, High School
    A Tale of Two Transformations
    Compare the results of these two transformations on the coordinate plane.
    Geometry 6th to 8th, High School
    A Tangent Square and Circle
    The square and circle below are tangent at one point and meet at four other points, as shown in the picture. If the side of the square is 8 units long, what's the radius of the circle?
    Geometry 6th to 8th, High School
    A TriangleSquare Ratio
    A square with side length s is inscribed in an equilateral triangle of side length t. Find the ratio of (t/s), accurate to four places to the right of the decimal.
    Geometry 6th to 8th, High School
    A Triangular Garden
    Cynthia has two pieces of garden edging. One is 8' long and the other is 6'. Will a third side of 12' or 11' make a triangle with a larger area?
    Geometry 6th to 8th, High School
    Added Areas
    A circle and an isosceles triangle are inscribed in a square. If the areas of the three figures added together is 28 square units, what's the edgelength of the square?
    Geometry 6th to 8th, High School
    All Around the World
    If a wire wrapped around the equator of the Earth is lengthened, 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?
    Geometry 6th to 8th, High School
    An Inscribed Circle
    A circle is inscribed in a triangle with sides of 6, 6, and 4. What's the radius of the circle?
    Geometry 6th to 8th, High School
    Analyzing Angles
    Given some information about angles in a picture, figure out some of the angle measures.
    Geometry 6th to 8th, High School
    Another Ambiguous Angle
    Given isosceles triangle ABC, with BE perpendicular to AD. If angle ACB is x, what is angle CBE?
    Geometry 6th to 8th, High School
    Ants Marching
    Traveling along the edges of a cross section of the cube, find the length of the shortest possible path from one corner of a cube to the opposite corner, as well as the longest possible path between the same corners.
    Geometry 6th to 8th, High School
    Approximating Pi
    Approximate the value of pi using polygons instead of a circle.
    Geometry 6th to 8th, High School
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