Sine rule and cosine rule

  • Square World
    problem

    Square world

    Age
    16 to 18
    Challenge level
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    P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
  • Get Cross
    problem

    Get cross

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
  • Quadarc
    problem

    Quadarc

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.
  • Biggest Bendy
    problem

    Biggest bendy

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
  • Bendy Quad
    problem

    Bendy quad

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
  • Just touching
    problem

    Just touching

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    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 Dodecahedron Explained
    article

    The dodecahedron explained

    What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?