Categories
Intermediate

Fan of cards

N coloured rectangular cards are arranged with a common vertex and common angle α between cards. If a single card has perimeter P, what is the perimeter of the coloured region, in terms of N, P, and α?

Extra condition: N and α are such that at least two edges of the bottom card are visible.

Categories
Intermediate

Shine your light

A quarter circle of radius 1, a rectangle touching the circle in an arbitrary point and a yellow quadrilateral. What is the minimal perimeter of this quadrilateral?

Categories
Intermediate

A light packing

A triangle containing two congruent squares. Each square has 1/3 the perimeter and 1/6 the area of the triangle. What’s the triangle side length proportion a : b : c?

Categories
Intermediate

Ceteris paribus

Three circles with their centres and a triangle ABC. Given that D is the midpoint of BC, prove that quadrilateral ABEF and triangle ECF have both equal perimeter and equal area.

Categories
Advanced

Slightly skewed

Two overlapping equilateral triangles with side lengths 1. What is the total red length?

Categories
Beginner

The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

Categories
Advanced

The Post-it note

Two unit squares (having side 1) are placed as shown. What is the total perimeter of the two red triangles?