Given a point A on a circle and another point I in the interior of the circle, find two other points B, C on the circle so that I is the incentre of the triangle ABC. Find B and C as the intersection points between the given circle and some other circle.
A regular pentagon and two equilateral triangles. What’s the angle α?
What is the area of the entire figure (in terms of x) given that the segments AB, CD, EF,…, QR are all semicircle diameters, and the lengths decrease geometrically ( AB=2, CD = 2x, EF= 2x^2, GH = 2x^3,…)?
A square containing a rectangle. What is the red fraction?
Three squares and a regular pentagon. Prove that the three red vertices are collinear.
Two squares and some line segments. Find the relation between the angles α and β.
How does the average of the areas of the blue and green squares compare with the area of the purple square?
Given green and blue discs, construct a red region so that for every ray leaving L stays in the blue region exactly as long as it does in the pink region. (Namely, KM = OL.)
A quarter circle with a right triangle. Prove that the red point is the incentre of this triangle.
Five squares and a diagonal. What fraction of the largest square is coloured?
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