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?

# Tag: triangle

## Stuck in the corner

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

## 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?

## Missing an angle

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

## Euclid’s wing

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

## Making a dent

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

## Pines and sky

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

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

## The grassy knoll

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