Categories
Intermediate

Harmonic proportions

A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.

Categories
Intermediate

The crazy quilt

A parallelogram is divided into several areas. What is the area X of the blue trapezium?

Categories
Intermediate

The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?

Categories
Beginner

Parallelism

A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?

Categories
Intermediate

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.

Categories
Intermediate

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?

Categories
Intermediate

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?

Categories
Beginner

The leaning tower

A trapezium with it’s diagonals. Two areas are given. What faction is coloured?

Categories
Intermediate

The three rights

A trapezium containing three right angles is split in two. What is the proportion of the areas yellow : blue?

Categories
Intermediate

The paper hat

A rectangle and several triangles. The orange triangle has the same area as the green trapezium. What’s the total coloured fraction?