Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral?
Blue circle (ACDGB) with CEG || AB. Pink circle (EDG) intersects AB at I. Extend DI to intersect blue circle at J, then JC intersects AB at M. Show that IM = CE.
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.