A semicircle with its centre. What is green : red in terms of the angles α and β?

# Tag: proportion

## Snow man scarf

Show that blue = red if and only if purple = orange.

## 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?

## 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.

## Wild floor tile

What is the ratio of areas, purple/green, when the orange octagon is regular (all angles equal)?

## Euclid’s wing

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

## The gondola lift

A tangent and its normal in an arbitrary point on an ellipse with eccentricity e. The focal points are also shown. What is the minimum value of blue : red in terms of e?

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

## The tipi entrance

A semicircle with three tangents. Prove that purple : green = red : yellow.