A regular pentagon and a right triangle. What’s the angle α?

# Tag: triangle

## Bond of union

Two intersecting circles with two inscribed triangles and two line segments through an intersection point. Prove that the triangles are similar.

Co-author: Marshall W. Buck.

## Centre of attraction

An equilateral triangle with two perpendiculars to a point that is at the same height as the triangle centre. What is red : yellow?

## The chessboard hallucination

Behold a 13-14-15 triangle. The 15-long side is dissected into 5 equal parts and the 14-long side is dissected into 7 equal parts. What is the difference between the red and green areas?

Author: Marshall W. Buck.

## The personal letter

Two rectangles share two vertices. What’s the green fraction?

## The right position

A triangle, its incircle and a right triangle. The circle centre is shown in blue. Prove that the tangency points and right triangle vertex are collinear.

## The Pythagoras bug

Two blue squares and two red right triangles. What are the proportions of the triangle sides?

Author: Matthew Arcus.

## The Suresh triplet

Two squares share a vertex. What’s blue : green : orange?

An equilateral triangle and three line segments. What’s the angle α?

## The prisoners dilemma

Two prisoners are chained to the walls of a triangular cell. The base is covered with a mirror and a perpendicular wall is separating them. They can each see the opposite corner through a hole. Proof they can see each other through another hole at the base of the perpendicular.

Proposed by Marshall W. Buck. Note that this problem is known as the Blanchet Theorem.