Two congruent circles and a triangle. Prove that the triangle is isosceles.
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?
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?
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.
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?
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?
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?
The intersection
Two intersecting circles. Prove that the three blue line segments are of equal length.
All the marbles
A circle containing eight touching circles. Circles of equal colour are congruent. What fraction of the total area is coloured?
The drunk spider
A circle with several chords forming four coloured triangles. What is the proportion yellow : purple?