Categories
Intermediate

Hang a right

Two circles, one having its centre on the other, and four line segments. Prove that the three coloured line segments are congruent.

Categories
Intermediate

Methane

Four orange unit circles and their red centres. What is the radius of the green circle? Kindly provided by Marshall W. Buck.

Categories
Intermediate

Rule of 72

Two triangles and an extended side. What’s blue : orange?

Categories
Beginner

Sailing by night

A circle with an inscribed quadrilateral. Prove that ab=cd. Kindly provided by Marshall W. Buck.

Categories
Advanced

The hawfinch II

A circle with two tangents. What’s red : blue in terms of α?

Categories
Advanced

Count to five

A triangle with a cevian. What’s α?

Categories
Intermediate

The truss bridge

Two lines connected by five triangles. Prove that orange = blue. Created by Marshall W. Buck.

Categories
Intermediate

The sandal

A triangle with two angular bisectors. What’s the proportion blue : red?

Categories
Beginner

Diamond life

Two equilateral triangles and one centre. What’s green : red?

Categories
Advanced

The Moroni minimum

An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?