Show equality of the green and orange square playing field areas.
Video: The punctured hexagon
The doubleganger
Two nested right triangles with their incircles. Two tangency points are shown. Prove that the red and yellow line segments are parallel.
Video: Wedge the wedge
The hippodrome shadow
The racer at A is running counter-clockwise around the inside of the outer purple circle, with a “shadow racer” B following behind, related by the three chords that are tangent to the inner orange circle. Does the shadow B ever catch up with A?
Cherries
Two tangent circles and two green tangents. The three tangency points are shown in black. Prove that the blue line segment is a common tangent.
Video: Blowing bubbles
Sticky corners
Two equilateral triangles and several line segments. What is red : yellow?
Median between sides
A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given the lengths (a,b,f) construct the triangle. (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)