2D shapes and their properties

  • Small pepper seedlings in turquoise pots.
    problem

    Roll On

    Age
    14 to 16
    Challenge level

    Weekly Problem 5 - 2006
    How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

  • Small pepper seedlings in turquoise pots.
    problem

    Semicircle in a Semicircle

    Age
    14 to 16
    Challenge level

    The diagram shows two semicircular arcs... What is the diameter of the shaded region?

  • Small pepper seedlings in turquoise pots.
    problem

    Oh so Circular

    Age
    14 to 16
    Challenge level

    The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

  • Bicentric Quadrilaterals
    problem

    Bicentric Quadrilaterals

    Age
    14 to 16
    Challenge level
    Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
  • Small pepper seedlings in turquoise pots.
    problem

    Circle Time

    Age
    14 to 16
    Challenge level

    Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

  • Pent
    problem

    Pent

    Age
    14 to 18
    Challenge level

    The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

  • 2D-3D
    problem

    2D-3D

    Age
    16 to 18
    Challenge level

    Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?

  • Circles in Circles
    problem

    Circles in Circles

    Age
    16 to 18
    Challenge level

    This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.

  • Just touching
    problem

    Just Touching

    Age
    16 to 18
    Challenge level

    Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

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