A square containing four smaller squares. What fraction of its area is orange?
Categories
Confined enclosure
Categories
Lean on me
Two squares and two diagonals. Prove that the angles α and β are equal.
Categories
The sacrosanct circles
Two tangent circles and two tangent line segments meeting in a point on the outer circle. The tangency points are connected by a line segment of length x. What’s x in terms of a and b?
Categories
The sliding ladder
A ladder seen from the side is sliding down a wall. Prove that a fixed point on the ladder traces part of an ellipse.
Categories
Check and balance
A square divided by three line segments. The red and blue areas are equal. What’s the length proportion a : b?
Categories
The dolphin
Two semicircles, a tangent and an altitude to the tangency point. Prove that the red triangle is isosceles.
Categories
Extreme parallelism
Four parallel line segments, one of which is divided in three parts. What is the proportion blue : red : green?
Categories
Parallelism
A trapezium with its diagonals and a parallel line segment. What’s the proportion blue : red?
Categories
Squaring the circle
Two perpendicular squares inside a circle. The circle centre is located on the side of one square. The line segment connecting two vertices has length a. What is the circle area?
Categories
The inner diamond
A triangle with side lengths a and b and an inscribed rhombus. What is the blue fraction in terms of a and b?