A square with an extended side. What’s the angle α?

# Author: Rik

## Along similar lines

The blue triangle is similar to the green one and has the same orientation. The midpoints between corresponding vertices are connected to form a red triangle. Prove that it is also similar.

## Methane

Four orange unit circles and their red centres. What is the radius of the green circle? Kindly provided by Marshall W. Buck.

## Rule of 72

Two triangles and an extended side. What’s blue : orange?

## The bubble chamber II

A square with a diagonal and two circles. What is the area proportion of the two circles?

## Sailing by night

A circle with an inscribed quadrilateral. Prove that ab=cd. Kindly provided by Marshall W. Buck.

## The hawfinch II

A circle with two tangents. What’s red : blue in terms of α?

## Outside the frame

Two squares and an equilateral triangle. Prove that the area of the triangle plus the small square equals that of the large square.

## The odd balance

Two circles are tangent to two perpendicular lines and have their centres connected. Prove that the green triangle is right isosceles.

## The stack

Three squares and three line segments. What’s the angle α?