A regular hexagon and two equals angles. What is blue : green : red?

# Tag: length

## Skimpy bathing suit

An equilateral triangle with a circle through one vertex, and the intersections FIHJ of the extended sides with the circle. Lengths of three of the external segments are indicated. What is the fourth length?

## Mother’s umbrella II

A circle with several line segments. The red one is tangent. What’s red : green?

## Distant Alp II

A square with its diagonal. Prove that the three red points are collinear.

Blue and orange concentric circles intersect a vertical line in green dots. Show that the dots are equally spaced, given that the red intervals shown are of equal length. (The largest circle has radius 2u.)

## Hidden parallelogram

Blue circle (ACDGB) with CEG || AB. Pink circle (EDG) intersects AB at I. Extend DI to intersect blue circle at J, then JC intersects AB at M. Show that IM = CE.

## Cradle of waves

What is the area of the entire figure (in terms of x) given that the segments AB, CD, EF,…, QR are all semicircle diameters, and the lengths decrease geometrically ( AB=2, CD = 2x, EF= 2x^2, GH = 2x^3,…)?

## Double eclipse

Given green and blue discs, construct a red region so that for every ray leaving L stays in the blue region exactly as long as it does in the pink region. (Namely, KM = OL.)

## Steam roller

Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

## Pentagon pleasure

Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?