An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?
The bear trap
A semicircle with two tangents and a perpendicular line segment from a tangency point. What is the blue area in terms of lengths a and b?
The road less traveled
What is the area of the trapezium in terms of lengths a and b?
A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.
The crazy quilt
A parallelogram is divided into several areas. What is the area X of the blue trapezium?
A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?
A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?
Pulling the strings
Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.
The wall between us
Two circles inscribed an a trapezium divided by a perpendicular line segment. What is the proportion of its length a and the side b?
The green trap
A circle with its centre in the origin is cut by two parallel lines that are a distance d apart. One line is passing through the leftmost and one through the lowest point of the circle. What is the area of the green trapezium in terms of d?