Circle properties and circle theorems

problem
Favourite

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
Favourite

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

Crescents and Triangles

Age

14 to 16

Challenge level

Can you find a relationship between the area of the crescents and the area of the triangle?
problem
Favourite

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
Favourite

Baby Circle

Age

16 to 18

Challenge level

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
problem

Set Square

Age

16 to 18

Challenge level

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
problem
Favourite

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.