Categories
Beginner

Family ties

Two regular pentagons share a vertex. What is the proportion red : green?

Categories
Intermediate

Mother and child

Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c?

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

The glass splinter

A triangle of which two sides and one angle are given. What’s the angle α?

Categories
Advanced

The Christmas star

Two congruent concentric equilateral triangles. Prove that the gold fraction is red/blue.

Categories
Intermediate

Pushing the boundary

Two equilateral triangles are placed side by side. What’s the proportion green : red?

Categories
Intermediate

A deep connection

Two squares inside a circle. What is the circle area in terms of length a?

Categories
Advanced

Square one

Three squares share a vertex. Two line segments pass through side midpoints. Prove that a : b = c : d.

Categories
Intermediate

The japanese progression

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?

Categories
Intermediate

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?