Categories
Intermediate

Tangent latitudes

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?

Categories
Advanced

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.

Categories
Intermediate

Perspective

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

Categories
Advanced

Siamese triplet III

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

Categories
Intermediate

Consecutive numbers

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

Categories
Intermediate

Hex division II

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

Categories
Intermediate

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?

Categories
Intermediate

Mother’s umbrella II

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

Categories
Advanced

Distant Alp II

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

Categories
Beginner

Bullseye

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.)