A quadrilateral and a parallelogram share two sides, and a vertex from each determine the orange square. The lengths BC, EF, AD are 4,5,7 respectively, where E and F are midpoints of AB and DC. What is the orange area?
Several line segments, some of which are parallel. What is green : orange?
Four squares and one centre. Prove that the red quadrilateral is a parallelogram.
Four equilateral triangles. Two centres are shown. Prove that the green quadrilateral is a parallelogram.
A parallelogram and four equilateral triangles. What is yellow : green?
A pink parallelogram with two extended sides. What’s α : β?
Four equilateral triangles. Prove that the red quadrilateral is a parallelogram.
Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.
Three parallelograms are inscribed in a circle. Prove that the common red vertex is the orthocentre of the dashed triangle.
A parallelogram ABCD with a circle and a diameter CE. Prove that point E is the orthocentre of triangle ABD.