A square with a diagonal and a right triangle. What’s the proportion blue : red?
Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?
A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?
A triangle with its circumcircle and circumcentre. What’s α : β?
In this right triangle, if red = blue, what is orange : purple?
A quadrilateral with its diagonals. What’s the angle α?
An orange square and a blue rectangle with two congruent inscribed circles. What is the angle α?
Two circles and three coloured isosceles triangles. Prove that the circles are concentric.
Three semicircles and a circle with their centres. Two orange ellipses with focal points in the semicircle centres (they share the middle one). Prove that their upper intersection point coincides with the circle centre.
Three semicircles and a circle. Three centres are shown in green. What’s the proportion red : blue?