Triangles

  • ArRh!
    problem

    ArRh!

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

  • Xtra
    problem

    Xtra

    Age
    14 to 18
    Challenge level
    filled star empty star empty star
    Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
  • Two triangles in a Square
    problem

    Two triangles in a square

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
  • Hexy-Metry
    problem

    Hexy-metry

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

  • A Shade Crossed
    problem

    A shade crossed

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
  • Triangle Island
    problem

    Triangle island

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?
  • Circumnavigation
    problem

    Circumnavigation

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
  • Threesomes
    problem

    Threesomes

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
  • Diagrams
    problem

    Diagrams

    Age
    7 to 11
    Challenge level
    filled star filled star empty star
    A group activity using visualisation of squares and triangles.