Two squares share a vertex. One line segment connects their centres, another two vertices. What is the length proportion blue : red?
Month: June 2022
The wall socket
Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
The remote corner
A square and a circle. What is the green area?
The sneak peek
A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
Fair and square
Two squares of which three vertices form an isosceles triangle. What is the angle α?
The double helix
Five equidistant parallel line segments. What’s the proportion green : red?
The push-up
Two squares share a vertex. What’s the proportion x : y in terms of side lengths a and b?
The glass ceiling
Three squares, two of which share a vertex. What is the total area?
The golf ball
A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.
The triangle pull
An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x?