Circle properties and circle theorems

  • 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.
  • Perfect Eclipse
    problem

    Perfect Eclipse

    Age
    14 to 16
    Challenge level
    Use trigonometry to determine whether solar eclipses on earth can be perfect.
  • Fixing It
    problem

    Fixing It

    Age
    16 to 18
    Challenge level

    A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?

  • Set Square
    problem

    Set Square

    Age
    16 to 18
    Challenge level

    A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

  • 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?

  • The Cyclic Quadrilateral
    article

    The Cyclic Quadrilateral

    This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.
  • Placeholder: several colourful numbers
    page

    Circle Theorems

    This set of resources for teachers offers interactive environments which support work on properties of angles in circles at Key Stage 4.
Displaying 41 - 49 of 49