A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.
Month: November 2022
Letting go
Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?
Orange above
A square contains a right triangle. What fraction is orange?
The double flag
Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?
The door stop
A triangle with a cevian. What is α?
Four to twelve
A regular dodecagon and a square share two vertices. What is the area proportion square : dodecagon?
The japanese progression
An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?
The triangular tiling
A rectangle is divided into four similar triangles. What fraction is blue?
The righteous four
Four rectangles. The green and red rectangle are similar. What’s the area proportion of the orange and the blue rectangle?
The gyroscope
Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.