A circle with its centre and several line segments. The red one is a tangent. What is the angle α?

## Cozy in his chair

Orange and green semicircles with equally long but perpendicular diameters (both length 2) are partially covered by a blue canopy at angle α. What is the orange area, which is not covered by either of the other regions, in terms of α?

## The double iglo

Two semicircles with their centres. What’s the angle α?

## Stuck in the corner

A square with a diagonal and a right triangle. What fraction is red?

## Five tangents

Five points ABCDE are equally spaced around the dotted circle. A smaller red circle is tangent to (ABCDE) at a point F, between B and C. Blue and green tangents are drawn from ABCDE to the red circle, and are coloured blue and green as shown. Show that the length sum of the blue tangents equals the length sum of the green tangents.

## Four square

Four squares. The red vertex is the centroid of the red triangle. What is the yellow area?

## The propeller

The blue square blades are twice as long as the red triangle sides. What is the ratio of red to yellow areas?

## Connected centres

Two quarter circles and a semicircle. The blue points are quarter and semicircle centres. What is red : green?

## Missing an angle

A triangle with three line segments to an internal point. What’s the angle α?

## Seven chords

A regular 7-gon inscribed in a circle (ABCDEFG), with some other point H on the circle, in the arc CD. Show that the length sum of the blue chords equals the length sum of the green chords.