Categories
Intermediate

The fish bowl

A circle with an inscribed triangle, a tangent and two bisected angles. What is the length proportion of the red and green line segments?

Categories
Intermediate

House of the rising sun

A semicircle, a circle, a square and an equilateral triangle. The two points are the tangency point and the semicircle centre. What fraction of the total area is yellow?

Categories
Advanced

The square of Amaresh

A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.

Categories
Intermediate

Il tricolore

Two squares share two vertices. A line segment connects two other vertices, forming the base of three triangles. What is the proportion green : white : red?

Categories
Beginner

The French kiss

Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?

Categories
Advanced

Stuck in the middle

A right triangle with semicircles along its perpendicular sides having lengths a and b. Two smaller inscribed circles. What is the proportion blue : red in terms of a and b?

Categories
Intermediate

The intersection

Two intersecting circles. Prove that the three blue line segments are of equal length.

Categories
Intermediate

All the marbles

A circle containing eight touching circles. Circles of equal colour are congruent. What fraction of the total area is coloured?

Categories
Beginner

The drunk spider

A circle with several chords forming four coloured triangles. What is the proportion yellow : purple?

Categories
Beginner

That hill

A triangle is divided in three smaller triangles. What is the proportion yellow : green?