Categories
Beginner

The pine forest

A square containing a quarter circle. What’s the proportion blue : brown : green?

Categories
Beginner

The star gazer

A square divided by a diagonal and another line segment. What fraction of its area is purple?

Categories
Advanced

The Eightfold Path

A semicircle, a square and an isosceles triangle. What’s the angle α?

Categories
Intermediate

The augmented chord

A circle with four chords. What is the length of line segment x in terms of lengths a and b?

Categories
Beginner

The dome tent

A rectangle with a diagonal and an inscribed semicircle. What is red : green : blue?

Categories
Advanced

Fun with flags

A triangle with two cevians. What is d/c-b/a?

Categories
Intermediate

The tightrope dancer

A circle containing an isosceles and two equilateral triangles. What is the proportion orange : blue?

Categories
Intermediate

The hidden pyramid

A triangle with an inscribed equilateral triangle. If areas A and B add up to C, what are the proportions A : B : C?

Categories
Advanced

The Olympic bowl

A parabola is tangent to the equal sides of an isosceles triangle in its equal vertices. Another tangent is drawn as shown. Prove that the red line segments are congruent.

Categories
Advanced

As above, so below

A semicircle, a square, a triangle and two circles. A centre and a tangency point are highlighted. Prove that the circles are congruent.