A ray of light is emitted from a point on the wall of a mirror-covered semicircle and reflects four times as shown to return to the same spot. If the radius is 1, what is the length of the path?
A unit square paper is folded as shown. What is the red area?
What is the locus of orange points for which the purple lines are parallel? The fixed cevians of the triangle BCD are angle bisectors.
A right triangle with two angle bisectors. What is red : blue?
A regular hexagon of which the centre is a vertex of an equilateral triangle. What is the angle α?
Several triangles and three congruent angles. Prove that the red point is the incentre of the yellow triangle.
A boatsman races to cross Isosceles Bay five times, finishing at End. A bicyclist pedals around the bay. How many times faster must the bicyclist travel in order to be sure to beat the boat to End?
A rectangle inside a rectangle. What is the green area?
Two equilateral triangles are placed side by side. The common (blue) side is extended. What is red : blue?
Two squares and a circle. The line through the big square centre and small square vertex is tangent to the circle. What is the red area?