Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Do points P and Q lie inside, on, or outside this circle?
