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

# Tag: triangle

## The star gazer

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

## The Eightfold Path

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

## The augmented chord

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

## The dome tent

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

## Fun with flags

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

## The tightrope dancer

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

## 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?

## 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.

## 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.