Two semicircle sit on the diameter of a semicircle centre O of
twice their radius. Lines through O divide the perimeter into two
parts. What can you say about the lengths of these two parts?
M is any point on the line AB. Squares of side length AM and MB are
constructed and their circumcircles intersect at P (and M). Prove
that the lines AD and BE produced pass through P.
The circumcentres of four triangles are joined to form a
quadrilateral. What do you notice about this quadrilateral as the
dynamic image changes? Can you prove your conjecture?
There is something special about a triangle with sides of $8,
15$ and $17$.
The sides of the triangle are tangents to the circle.
You might like to look at how to construct an inscribed circle in
the Thesaurus (Search under constructions).
The angle between a tangent and a radius is $90^\circ$ .
The centre of the inscribed circle lies on the bisector of the
angle between the two tangents from any point outside the
The two tangents to a circle from the same point are equal.