Two coloured triangles share a vertex. Prove that the red line segments are parallel.
Categories
Between the lines
Tag: angle
Categories
Drop shadow II
A right isosceles triangle contains another triangle. What is the angle α? Advanced if no trigonometry is used.
Categories
The telescope
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?
Categories
The weight lifter
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.
Categories
Outside the pentagon
A regular pentagon and two coloured equilateral triangles. What is the angle α?
Categories
Baby block II
A square containing another square with an extended side. What is tan(α) in terms of the red and green segment lengths?
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
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?