Ratio and proportion

  • Chord
    problem

    Chord

    Age
    16 to 18
    Challenge level

    Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

  • Halving the Triangle
    problem

    Halving the Triangle

    Age
    16 to 18
    Challenge level

    Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.

  • Extreme dissociation
    problem

    Extreme Dissociation

    Age
    16 to 18
    Challenge level

    In this question we push the pH formula to its theoretical limits.

  • Another Triangle in a Triangle
    problem

    Another Triangle in a Triangle

    Age
    16 to 18
    Challenge level

    Can you work out the fraction of the original triangle that is covered by the green triangle?

  • Five circuits, seven spins
    problem

    Five Circuits, Seven Spins

    Age
    16 to 18
    Challenge level
    A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
  • Striking gold
    problem

    Striking Gold

    Age
    16 to 18
    Challenge level

    Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.

  • Golden Ratio
    problem

    Golden Ratio

    Age
    16 to 18
    Challenge level

    Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

  • Rarity
    problem

    Rarity

    Age
    16 to 18
    Challenge level

    Show that it is rare for a ratio of ratios to be rational.

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