Angles in polygons

  • Small pepper seedlings in turquoise pots.
    problem

    Angle to Chord

    Age
    14 to 16
    Challenge level

    Weekly Problem 23 - 2008
    A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

  • Small pepper seedlings in turquoise pots.
    problem

    Circled Corners

    Age
    14 to 16
    Challenge level

    Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

  • Small pepper seedlings in turquoise pots.
    problem

    Incentre Angle

    Age
    14 to 16
    Challenge level

    Weekly Problem 1 - 2011
    Use facts about the angle bisectors of this triangle to work out another internal angle.

  • Small pepper seedlings in turquoise pots.
    problem

    Wood Pile Perimeter

    Age
    14 to 16
    Challenge level

    Weekly Problem 30 - 2011
    Three touching circles have an interesting area between them...

  • Angles in Three Squares
    problem

    Angles in Three Squares

    Age
    14 to 16
    Challenge level
    Drawing the right diagram can help you to prove a result about the angles in a line of squares.
  • No Right Angle Here
    problem

    No Right Angle Here

    Age
    14 to 16
    Challenge level

    Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

  • Pentakite
    problem

    Pentakite

    Age
    14 to 18
    Challenge level

    Given a regular pentagon, can you find the distance between two non-adjacent vertices?

  • 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.

  • Road maker 2
    problem

    Road Maker 2

    Age
    16 to 18
    Challenge level

    Can you work out where the blue-and-red brick roads end?

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