An equilateral triangle and a parabola that is tangent to two of its sides in two vertices. Proof that the triangle centre coincides with the parabola focus.
The skewed tree
A triangle with a line segment through its centroid and parallel to a side. What faction is dark green?
A deep connection
Two squares inside a circle. What is the circle area in terms of length a?
Square one
Three squares share a vertex. Two line segments pass through side midpoints. Prove that a : b = c : d.
To shy away
Two squares share a vertex. What’s the proportion orange : blue?
The domino effect
Two overlapping congruent rectangles. What’s the angle α?
Squaring a rectangle
A regular hexagon, a square and a rectangle. What is the area proportion rectangle : square?
A clear vision
A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?
Star and stripes
Two concentric congruent squares and two red rectangles. What fraction of the total area is red?
The inner parallel
A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.