A triangle with its excircles. The tangent radii are extended. Prove that the red line segments are concurrent and congruent.

# Tag: circle

## Snow man scarf

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

## Lemon slice II

A semicircle inscribed in a quarter circle. What fraction is yellow?

## Cuckoo in the nest

Two tangent semicircles inscribed in another semicircle. What is the total area?

## The tritium nucleus

Three discs are mutually tangent among themselves and with an enclosing circle of radius 18. The blue circle has radius 9. What it the common value of the radius of the gray discs?

## The sundial

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?

## 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.

## Connected centres

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