N coloured rectangular cards are arranged with a common vertex and common angle α between cards. If a single card has perimeter P, what is the perimeter of the coloured region, in terms of N, P, and α?
Extra condition: N and α are such that at least two edges of the bottom card are visible.
Two coloured triangles share a vertex. Prove that the red line segments are parallel.
A right isosceles triangle contains another triangle. What is the angle α? Advanced if no trigonometry is used.
The odd regular polygons are stacked together, in increasing order, zigzagging to form a telescope that extends forever! What is the limiting angle (with respect to the horizontal) at which the telescope points?
Three squares sharing two vertices. Prove that the three red vertices are collinear.
Express the x coordinate of E in terms of x coordinates of A, B, F, and G. The two black lines are supposed to be parallel to the x-axis.
A rectangle with three line segments. What fraction is blue?
Four equilateral triangles. Two centres are shown. Prove that the green quadrilateral is a parallelogram.
Two equilateral triangles, one upside down, have boundaries meeting at 4 points, 3 of which are marked in red. Show that the circle through the red points also passes through the centre point of the blue triangle.
A regular pentagon and two coloured equilateral triangles. What is the angle α?