Categories
Intermediate

Parallel universes

Two straight lines are specified by y=a+cx and y=b+cx, respectively, where b≥a. What’s the distance d between them in terms of a, b and c?

Categories
Beginner

Below the line

Two squares share a vertex at the origin and have their sides along the x- and y-axis. Two vertices lie on the line satisfying x+2y=c. What is the proportion purple : yellow?

Categories
Intermediate

Between the bars

Two parallel lines support two rectangles. Prove they have equal area.

Categories
Advanced

The fallen pine

Two congruent isosceles triangles and three lines. Prove triangle AEF is also isosceles.