Explaining, convincing and proving

problem
Cyclic quad jigsaw

Age

14 to 16

Challenge level

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?
problem
Angle trisection

Age

14 to 16

Challenge level

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
problem
Lens angle

Age

14 to 16

Challenge level

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
problem
Hexy-metry

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
problem
Far horizon

Age

14 to 16

Challenge level

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
problem
Harmonic triangle

Age

14 to 16

Challenge level

Can you see how to build a harmonic triangle? Can you work out the next two rows?
problem
Partly circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?
problem
Close to triangular

Age

14 to 16

Challenge level

Drawing a triangle is not always as easy as you might think!
problem
Geometric parabola

Age

14 to 16

Challenge level

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.