Tangent lines QC and EC meet at C. A point D on QC has DC=1 and QD=2. The line ED intersects the circle at G, and the line HGI is parallel to QDC. What is HG/GI?

# Tag: length

## Flying saucer II

If X is the midpoint of the segment connecting the centers of the upper and lower arcs, and JK is perpendicular to XH, then show that H is the midpoint of JK.

## Perspective

A is the center of a unit circle. What is the distance AG if the distance AC = x?

## Siamese triplet III

Three circles and a triangle. What is red : green?

## Consecutive numbers

A triangle with its incircle. What’s a : b : c?

## Hex division II

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

## 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.)