A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?
A square containing a quarter circle. What’s the proportion blue : brown : green?
Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.
Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?
A square divided by a diagonal and another line segment. What fraction of its area is purple?
A semicircle, a square and an isosceles triangle. What’s the angle α?
Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?
A circle with four chords. What is the length of line segment x in terms of lengths a and b?
A semicircle, a square and a chord. If the square has area 32, what is the semicircle area?
A rectangle with a diagonal and an inscribed semicircle. What is red : green : blue?