Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?
A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.
A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?
A regular hexagon with a diagonal and a circular arc centred in a side midpoint. What fraction is yellow?
A regular pentagon with an extended side. What’s the angle α?
A square with several line segments. Prove that the blue ones are parallel.
A square with an extended side inside another square. What fraction of the latter is blue?
Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c?
An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.
Three triangles are glued together. The green ones are based on a common line. What’s the angle α?