A rectangle containing three line segments. What fraction is blue?
Categories
Night mountain
Category: Beginner
The red and green wedges subtend the same angle, there are two right angles, and the blue sides have the same length. What is the ratio of lengths of the green and red segments?
Categories
Downhill skiing
Choose any point D on the side AB of an isosceles triangle ABC, then extend the side AC beyond C to a point F with |CF| = |DB|. Show that the segment DF is cut exactly in two by the third side BC—that the orange and red trails are equal.
Categories
Off the grid
A square on a grid containing a red triangle with an extended side. What is the red fraction?
Categories
Tip the scale
Two equilateral triangles and a square. What’s the angle α?
Categories
Rolling level
Blue and green circles with tangents. The green tangent line goes through the blue tangent point and the points IJH are collinear. Show that the blue and orange lines are parallel.
Categories
The camping
A square containing an isosceles triangle. What’s the angle α?
Categories
Hidden perfection
Two squares and two equilateral triangles. Prove that the red vertices also form an equilateral triangle.
Categories
All-seeing eye
If the radius shrinks by the factor 1/2 for each smaller circle, what fraction of the whole area is represented by all the blue crescents (separated by the red crescents)? Assume the circles keep going inward forever.
Categories
Launch the ball
Express the circle area in terms of the isosceles triangle area A and its side length a.