Month: March 2024
Squaring a rectangle II
A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.
Two medians and one side
A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given only the lengths (b,d,e) construct the triangle (a,b,c). (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)
Video: Unring a bell
Pentagon offspring
Three regular pentagons are placed as shown. Prove that the three black line segments are concurrent.
Wings
Two wings are attached to the corner of a rectangle, and have corners lined up with the diagonal of the rectangle. The angles at the lower wing tips are equal. Must α = β at the left wing tips?
Video: The doubleganger
Triangle offspring
Four equilateral triangles. Prove that the three black line segments are concurrent.
Video: Cherries
Crashing the kite
The orange lines are parallel, the purple lines are parallel, the dotted gray lines intersect the base at equal distances. What is the ratio of areas of the blue and green triangles?