Categories
Intermediate

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?

Categories
Intermediate

Stuck in the corner

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

Categories
Intermediate

Four square

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

Categories
Beginner

The propeller

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

Categories
Advanced

Missing an angle

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

Categories
Intermediate

Euclid’s wing

Several line segments, some of which are parallel. What is green : orange?

Categories
Intermediate

Making a dent

A right triangle with one trisected angle. What’s the angle α?

Categories
Beginner

Pines and sky

Show that the light blue area is the same as the dark green area.

Categories
Beginner

The bat

What is the full bat area (including the enclosed white parts) divided by that of its (equilateral triangular) upper torso?

Categories
Advanced

The grassy knoll

A triangle with three cevians that are concurrent in an arbitrary interior point. What is the maximum value of bdf/ace?