A circle with its centre and several line segments. The red one is a tangent. What is the angle α?
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?
Two semicircles with their centres. What’s the angle α?
A square with a diagonal and a right triangle. What fraction is red?
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 squares. The red vertex is the centroid of the red triangle. What is the yellow area?
The blue square blades are twice as long as the red triangle sides. What is the ratio of red to yellow areas?
Two quarter circles and a semicircle. The blue points are quarter and semicircle centres. What is red : green?
A triangle with three line segments to an internal point. What’s the angle α?
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.