Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
A square and a circle. What is the green area?
A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
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?
Three squares, two of which share a vertex. What is the total area?
A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.
An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x?
Two arbitrarily placed congruent equilateral triangles. Out of all the possible rotations of the plane, for how many will the image of ABC be A’B’C’?