Circle properties and circle theorems

problem
Three balls

Age

14 to 16

Challenge level

Do points P and Q lie inside, on, or outside this circle?
problem
Tied up

Age

14 to 16

Challenge level

How much of the field can the animals graze?
problem
Triangle incircle iteration

Age

14 to 16

Challenge level

Keep constructing triangles in the incircle of the previous triangle. What happens?
problem
Compare areas

Age

14 to 16

Challenge level

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
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
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
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
Bicentric quadrilaterals

Age

14 to 16

Challenge level

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
problem
Perfect eclipse

Age

14 to 16

Challenge level

Use trigonometry to determine whether solar eclipses on earth can be perfect.
problem
Belt

Age

16 to 18

Challenge level

A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.