Can you find the gradients of the lines that form a triangle?
Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.
Move the point P to see how P' moves. Then use your insights to calculate a missing length.
Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?
Given a regular pentagon, can you find the distance between two non-adjacent vertices?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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.
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.
Can you work out the fraction of the original triangle that is covered by the green triangle?
