Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
The wall socket

Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
Two squares of which three vertices form an isosceles triangle. What is the angle α?
Five equidistant parallel line segments. What’s the proportion green : red?
Two squares share a vertex. What’s the proportion x : y in terms of side lengths a and b?
An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x?
Five circles, of which the green circles are congruent and so are the blue ones. If rblue : rgreen= 6, what’s rred : rgreen?
A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?
A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?
A unit square with an extended side immersed in another square. What is the area of the red triangle?
Four squares, three of which are coloured. What’s the area of the blue one?