Show that the three red midpoints are collinear.
The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?
A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.
In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?
An orange circle is squeezed inside a rectangle. Show that no matter how the blue point moves on the circle, the derived points Q and P will satisfy |QL| = |KP|.
A regular pentagon with two extended sides and a right angle. What is blue : green?
Three congruent rectangles on a line. Prove that the four red points are cyclic.
Express the area of the orange triangle in terms of the areas of the other colours.
A triangle with two line segments. What’s the angle α?
Two intersecting circles with a triangle connecting them. Show that the three red points are collinear.