Show that the three red midpoints are collinear.
Categories
Lining up half way
Month: September 2023
Categories
The boomerang
A quadrilateral and a triangle. What’s the angle α?
Categories
The pentagon proportion
A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?
Categories
In touch
A regular nonagon and four equilateral triangles. The purple and yellow triangles share a vertex. Prove that the yellow triangles also share a vertex.
Categories
Running man
What is the area of the coloured figure? Can you determine the area without counting the number of squares in each different-coloured shape?
Categories
Baby steps
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?
Categories
The party hat II
An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?
Categories
The lighthouse
A parallelogram and four equilateral triangles. What is yellow : green?
Categories
Holes in my heart
The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?
Categories
Tip of the veil
A square with two right angles. What fraction is yellow?